I’m so sorry your parents aren’t supportive. I’ve had many letters like yours from teens whose parents don’t seem to see them for who they are. There are as many reasons as there are families. But regardless of the reason, it is painful and lonesome to feel like the people who should love you the most aren’t able to do so.
When that is the case, the best thing you can do is forgive them and love them for their strengths and look elsewhere for the support you need. With a straight A average, I’m guessing there must be a teacher or school guidance counselor who can help you look into scholarships for the summer program and for college in your future. Find out what private scholarships and grants are available. Then make sure you do the things you need to do to be eligible. That definitely means you need to keep high grades. If you aren’t already involved in a community service project, it would be a good idea to join one.
I’m glad you checked with your friends about your weight. Believe them. Your parents are not credible. For some reason, they don’t want you to feel good about yourself. Drop your end of the argument. It’s only making you miserable. Ignore their comments. They don’t matter. What matters is what you see in the mirror and what your friends say.
If you think it would be helpful, you could ask your counselor or teacher to talk to your folks. If you think it will only make matters worse, then don’t. Just go about the business of making a good future for yourself.
I wish you well.