Good luck on your brevet attempt!
200km, or 124 miles, is a long ride. For reference, on the road, average riders might complete a century ride (160km/100mi) in 5-7 hours, maybe less if one is with a fast group.
Note: I initially recommended that the OP drink ahead of thirst. In comments, @whatisname contended that this advice is based on a myth. On further research, I modified it.
Modifying my initial argument a bit: on a brevet, I recommend the OP drink at least until their thirst is slaked, but also consider electrolyte intake (described further below). Thirst alone can be a good guide for most people in most situations. However, the OP is not in a normal situation based on his proposed ride length. If it's hot, and especially if it's hot and humid, he may want to drink before perceiving thirst, or attempt to do so. Athletes should be aware that our thirst perception declines with age, so athletes over about age 65 should err on the side of drinking more as well. Athletes in cooler conditions should be fine drinking to thirst alone. I don't believe empirically measuring your fluid consumption is necessary, but it can be done, described in the next section.
Individual fluid consumption can vary a lot, but one can obviously start from a rule of thumb, e.g. one bottle per hour as proposed by @DavidW, and adjust based on your perception of thirst. (NB: cyclists also start with a rule of thumb and adjust as we go with bike fit parameters, e.g. saddle height and stem length.) With experience, you will find your own equilibrium. For example, in temperatures of 85F/30C and higher, I find that while I'm only 133 lbs/60.3 kg, I can drink as much as a 25oz/750ml bottle per hour. In temperatures around 70F/21C, my intake is more like 25oz/750ml per 1.5 hours.
British Cycling recommended that cyclists drink ahead of thirst, rather than just to thirst. They argued that thirst is a lagging indicator of your hydration status; when you feel thirsty, you are in a significant deficit. However, Allen Lim, who has worked extensively with professional road cyclists, countered on a podcast that these athletes were good at listening to their perception of thirst. He felt that perceived thirst was enough for them, and that they would generally hydrate themselves enough based on drinking to thirst. That said, these are professional athletes, and they train very extensively, so their perceptions of their bodies are well-developed.
Andy Blow, an exercise scientist writing for the TrainerRoad blog, argued that thirst alone is a good general guide in most exercise conditions. He argues that heat and exercise duration may modify this. I based my argument above on his post.
Measuring your fluid intake
Some of us might want to consider actually measuring our intake.
It appears that individual perspiration rates vary a lot, thus you may want a more accurate measure of your intake (alternatively, you might notice with experience that you need more fluid than your peers, or you might notice that you perform fine with less fluid).
Alternatively, a more empirical method like weighing onself before and after a ride of known duration (preferably in similar conditions as the event!), as the OP wrote, is also fine. This was proposed in an article by British Cycling, although they recommended a test period of 60 minutes. Naturally, you would need to adjust your intake up and down based on the weather and your own perception. Per this podcast interview with Allen Lim (referenced later), we would expect that most of the weight you lose should be through perspiration, rather than through burning stored glycogen or fat. If you eat, you then need to net out the weight of the food you ate.
The role of electrolytes, particularly sodium
The OP clearly seems to recognize the need for sodium already, but the discussion is incomplete without a mention of electrolytes, particularly sodium. You can take sodium in your fluid and/or your food.
Per the podcast interview cited earlier, we excrete sodium as we perspire. The rate at which we do this is highly variable, like sweat rates. If you don't replenish sodium, you will compromise your athletic performance. Thus, your drinks should contain some sodium.
As Lim discussed on the podcast, we may also develop a sense for how much salt we need. When I started cycling, I'd just stick to plain water, only to find that I'd crash at the end of long rides in the heat. This changed considerably when I started using electrolyte drinks, and when I paid attention to my diet's overall salt content. How much you crave salty food should be an indicator of low sodium. If you have very salty sweat, you will see salt deposits on your exercise gear after a long workout, or dogs may lick you after a workout. However, these may only indicate that you are a very salty sweater.
This ties into the role of carbohydrates in sports drinks
Carbohydrate in your drink may affect how well you absorb the fluid, but you do not want your drinks too sweet. Lim argued that a drink that is too concentrated (i.e. has too much sugar and other material dissolved) actually inhibited how well athletes could absorb the water content. Basically, the sports drinks had a higher concentration than our blood, and due to chemistry, this tends to pull water into your digestive tract rather than into your blood. Lim reported that many of his athletes developed bloating or other gastric distress from too-concentrated drinks. While you need to replenish carbohydrate stores while riding, I would not rely on sports drinks to do this.
Lim runs a company called Skratch Labs, and their drink mix contains about 20g of carbs (i.e. 80 calories) in a 16oz / 500ml drink. I'm unable to find consistent nutrition information for Gatorade on the web, but I believe this is half or less the amount in an equivalent Gatorade serving.
Specialist cycling hydration mixes are available, but they can be pricey, and you can brew your own. The section at the end of the answer has some suggestions.
What about fueling?
While the OP didn't ask directly, the discussion about carbs does naturally tie into the role of fueling during exercise. Cycling for very long distances burns a huge number of calories, and even Gatorade alone wouldn't be able to replenish them adequately. For example, during a solo century ride that took about 5h 30m of riding time, my power meter estimated that I burned about 2,700 calories. I weigh about 133 lbs. That's about 490 calories per hour. This was a fast ride (i.e. I was attempting to go as fast as I could; my intensity factor was 79% for those of you into power metrics). A slower pace will obviously burn less energy per unit time, and the OP should go at a slower pace for his first brevet. However, heavier individuals will naturally burn more energy.
Your body stores carbohydrates in the form of glycogen. You will deplete your glycogen stores after about 3 hours of cycling. If you don't replenish them, your performance will suffer (i.e. you are likely to bonk). Note that you also burn fat, and as exercise intensity increases, the ratio of fat to glycogen burned will increase (i.e. you burn proportionately less fat). However, you will still burn a lot of glycogen if you ride at an easy pace for 5 hours or more. For almost all athletes, our body's fat stores are adequate on their own. (NB: Ben Greenfield and Allen Lim discussed the potential for adding medium chain triglycerides, i.e. a form of fat, to food as a supplemental energy source; most of us should be fine with less sophisticated methods.)
You obviously don't need to replenish all the carbs you burn. In fact, in professional road cycling, riders physically couldn't digest enough food to accomplish that, even if they could eat that much in the heat of battle. Lim proposed that in his context, athletes could aim to eat about half the calories they actually burned per hour.
The OP may be trying to lose weight, but he will nonetheless want to have some simple carbs while riding. I would recommend at least 200 calories per hour. Fresh fruit, if available, contains water as well as carbohydrates, and it can make for a good healthy snack at rest stops (although take note that too much fiber on a long ride can upset your stomach, so it may be worth experimenting to see if you can tolerate this). Otherwise, energy gels and chews were developed for this purpose. If not that, then confections like chocolate bars or cookies will also work, although note that their fat content may also cause gastric upset (so, again, experiment if you're able).
(Side discussion: In some competitions, tactical considerations might make it hard to eat consistently. There are some highly-concentrated drinks that contain a lot of carbs in gel form that you might consider. Few of us are likely to need these. An example situation is a professional road race, where there may be numerous attacks throughout the race that riders have to respond to. In this context, respond means to get into the breakaway, or to ride with the peloton to retrieve the breakaway or to limit its time gap.)
A counterargument on drinking ahead of thirst
This answer initially advised to drink ahead of your thirst. @whatisname countered, in comments and in a separate answer, that this advice stems from a myth, and that one should focus on drinking solely to thirst.
Tim Noakes, interviewed in Outside magazine, is an exercise scientist who advised on the dangers of over-hydrating during long endurance events. Indeed, if you take in too much water without also taking in sodium, your blood sodium levels can drop too low (i.e. hyponatremia). This can be dangerous. In fact, a number of marathoners have died from hyponatremia.
Blow, on the TrainerRoad blog cited earlier, responded that Noakes may be exaggerating the evidence. Blow countered that there is significant evidence that many successful athletes take on supplemental sodium during exercise. Blow did agree that drinking plain water (i.e. no electrolytes added) was generally sufficient, emphasis mine:
And for many people training or racing shorter events in cool to moderate conditions, drinking water to thirst will be sufficient most of the time.
He also added that we have some room for error; if you under-hydrate on a two hour ride, you can push through and just drink more afterward.
However, he cautioned that if you're in a long event on a hot day, that's not really a normal situation. You may also have trained hard up to that event, and thus depleted your existing reserves. In this case, drinking plain water alone to thirst is not likely to be sufficient. Thus, I would advise electrolyte drinks in long events like brevets. Be aware that hyponatremia is possible, but you will need to drink lots of plain water while perspiring a lot.
For those of us who need low sodium intake due to blood pressure, I would advise consulting your physician. However, you will still need to replenish your electrolytes during long exercise. On the podcast, Lim discussed that there is a lab test that measures your sweat rate. It is normally done to detect cystic fibrosis, because people with CF excrete salt at abnormally high rates. For reference, Lim said that healthy individuals can excrete between 300 and 2,000 mg of sodium per liter of salt, whereas people with CF may excrete 3,500mg or more. This test could be worth considering if you really must closely calibrate your sodium intake. I believe that in most cases, you would need to approach your physician to take one.
Bonus content: Low-cost electrolyte drink mixes
Cycling-specific drink mixes can be very good, but they also can be pricey per serving. My favorite mix, Skratch Labs, is about US$1 or more per serving depending on how concentrated you mix it. I reserve it for major events.
You can brew your own electrolyte drinks. Abby Mickey, a former professional road cyclist and now a cycling journalist with Cyclingtips, provided one recipe using freeze-dried fruit or vegetable powder, salt, and maple syrup or sugar. Dave Everett, another Cyclingtips writer, provided recipes for drinks, an energy gel, and energy chews (the latter turned out "pretty damn terrible"). Last, I have taken powdered Gatorade, mixed it at half the recommended concentration, and added a pinch of table salt.
Bonus content 2: Hydration sensors
For some athletes, it may make sense to try a hydration sensor. These have a sensor unit plus a single-use patch attached to your skin via an adhesive. They should automatically measure and report your sweat rate and how much electrolytes you excrete. The Verge has a review of Nix's sensor here. The downside is the cost, and the fact that the patches are not reusable.
The Verge describes them as for "Type A" athletes. In principle, they could be used to establish your baseline sweat rate on a training ride. Then you could use that information to prepare a hydration strategy for your target event, e.g. how much fluids and which drink mix. I don't think that Nix currently pairs to Garmin or Wahoo head units, but if there's enough interest, those companies are likely to implement functionality. All electronic items decline substantially in cost as the demand increases, so the costs for hydration sensors might come down. However, I don't foresee how this could be anything other than a niche item (compared to the proliferation of power meters), but predicting the future is hard. Hence, I'm including this as something to perhaps watch out for.