Free stuff - start with your bike fit. Make sure your saddle height is high enough, but not so high your hips wiggle while pedalling.
Check brakes for rub - adjust brakes or true wheel if required.
Carry less stuff - wear fewer clothes when riding. Roadies tend to avoid big flapping jackets, and their clothes are more close-fitting.
Carry the right stuff - Water and some fuel is useful. A small thing like a lolly or a square of chocolate or a gel per hour of riding works for me for up to 3 hour rides, after that I need a more solid snack like a muesli bar or bliss balls.
Lock out any suspension on the road. Bobbing along slowly saps your power. If there is no lockout, then some bikes have tuneable suspension, so you can make them more firmer and loose less power. Downside is you still have to drag the useless suspension parts around with you, as excess weight.
Technique - look closely at others and see if you can observe differences between your technique and theirs.
Ride straight, but defensively - I see a lot of slower riders wiggling in and out of parked cars in the stationary lane. Turning reduces your forward speed, and ducking in between cars for a few metres is dangerous. So take a position on the road and ride in a straight line. Wear high vis colours and so on, but be perceptive to your surroundings in front and behind. I found the faster I go the further away from the kerb/curb I want to be. Be a door's width from parked cars. Ride with lights, even DRLs in the daytime.
Then a service - clean/lube your chain, clean your cassette, check wheel and BB axles for play/wobble. If you can do this yourself its free, otherwise its a service cost at the LBS.
Next options cost money, sorry.
New commuter tyres is your first and easiest gain. Inflate towards the higher end of the pressure range. Store your old tyres in case you want to take the bike on something offroad and gnarly someday.
Long term free things:
Carry less weight - Develop and implement a weight loss plan. I started at 105 kilos and have dropped to 95 over two years. This has certainly helped. However a lot of the weight loss has been offset with muscle mass.
Ride more/train more - Developing both fast and slow twitch muscle fibres will help with your raw burst power and your endurance respectively. This is not an overnight process, but better legs will totally help you go faster for longer.
Ride with others - Some of my best times have been gained while in pursuit of other riders. Organised rides help keep the motivation up, and show you routes or methods that could help you. Plus draughting/drafting can be a good 30% saving on your power input.
After that, you can look at getting more aerodynamic, but at some point you have to stop spending money to "put makeup on the swine" and start saving for a road bike.
As motivation, consider a lot of lighter road bikes have a maximum rider weight of 90 or 95 kilos, so consider setting this as a target weight before buying a new bike.
