Most important - Well done in losing weight, what you are experiencing is very normal, don't let it put you off.
A word of warning - despite the common perceptions, most people do not lose weight exercising. Their appetite increases to compensate for the the increased calorie demands, this could be what's happening to you.
Personally I think focusing on weight is at the expense of overall health and well being detracts from the progress most people make and demoralizes them needlessly. Take the weight loss as a part of the equation, but focus more on your fitness and progress. When you started, how far and fast, how often were you riding, how does that compare to now? Are you happier now? Focus on the wins.
Exercise builds muscle, which is heavier (and healthier) than fat - if the weight loss has leveled out because you are building muscle, keep doing what your doing. It may be too late, but measurement is a better guide to progress than weight - did you measure yourself before starting? If not, are your cloths looser, are they still getting looser? Are you feeling less flabby?
To continue to make progress you may need to mix it up a bit. Adding resistance exercises would help - I am a fan of body weight exercises - pushups, pull ups, squats, burpees etc will balance out the cycling. No need for expensive gym memberships and machines, the only thing most people are missing at home is a pullups bar.
As far as cycling, you can also mix it up - instead of training all the time at once pace, you need to have sessions of slow, long distance and sessions that are short, high effort. Also look at doing sprints after a good warmup, - 30seconds at absolute maximum effort, 30-60 seconds to recover, repeat 5 -10 times then cool down. Do these in a short session (if you do this properly, it will be short)
A good guide will be 3 - 4 sessions a week, one will be half you weekly distance at a steady, comfortable pace. One will be short and fast.
Have a look on the internet for suggest training program - they will look something like this:
Day 1 - 50% of weekly distance at slow steady pace
Day 2 - rest
Day 3 - 20% weekly distance at max effort
Day 4 - rest
Day 5 - rest
Day 6 - 30% weekly distance at 'race' pace
Day 7 - rest
One of my favorites - "You don't get fit exercising, you get get fit recovering from exercise."
Hopefully this is enough to get you started - there is a lot of information out there, some will not agree with what I believe. We are all different, sift though it and work out what's right for you. If what you doing does not work, or stops working, no matter who says it, change something.