How did you ask your parents?
I was 18 when I decided I wanted weight loss surgery. Our situations are different... when I asked my parents about the surgery - I wasn't just asking for permission, I was asking for the $$$... unfortunately my insurance company would not allow me to have the DS so I needed a LOT of $$$. Luckily, my parents were willing to help me and I've since had my surgery. I guess our situations differ also because my parents aren't triatheletes, rather they have struggled with weight issues throughout their lives - AND my mom had RNY 2 years before... So even though our situations are very different I can say this... be honest. Tell them how concerned you are with health risks due to your weight, tell them how you've tried to lose weight in the past, tell them how willing you are to follow post-op instructions... present your "case" to them with all of the info in mind. They will surely have questions so you NEED to have answers. Make sure you know what you're asking for. In my case, my parents were convinced by my knowledge of what I was getting myself into.
I would definitely find a doc. Even if he/she's not the "one", find a surgeon to discuss your options with. Again, this will give you information to present to your parents, giving them comfort and understanding of your seriousness about wanting this. GOOD LUCK to you!!