I'm another guy who started riding as a way to get some fun exercise and to lose weight. I do find that riding is a great way to lose weight, and yes, diet will also be a big part of the equation. I agree with the people who say that you don't need to make radical changes right now. You are just getting started with the exercise. Try to cut out the obvious stuff--fast food, soda, sweets, etc.
15 miles is a great start! I think that you will find that after a few weeks, you will be ready to add another mile or two to your rides, and moving up to 18 or 20 miles won't be an issue at all. Check with the bike shops in your town to see if there are any beginner group rides during the week. A lot of people who have been riding for years but don't consider themselves serious riders, will still ride in these. It's a great way to meet other people who ride and learn how to ride in a group.
Get some comfortable riding clothes too. I started out using bike shorts, but switched to bibs, which are much more comfortable. Find a couple on sale and them just wash them in the delicate cycle. That way you will always have something ready to wear when you want to ride.
Keep riding as much as you can, and your body will get stronger, and with consistency you will drop the pounds. I have lost 50 pounds in the past by riding regularly and limiting my diet a bit. I have also ridden a lot and eaten whatever I wanted, and not dropped a pound, so don't forget the diet part of it too.
Good luck!