Okay, yes, you have this whole thin privilege thing, and I'm not saying you shouldn't recognize this and recognize that being fat makes us fatties part of an oppressed group- an oppression that you, as a person with thin privilege, have an impact on.
What I'm saying is that I recognize the pain that comes with body dissatisfaction no matter what size you are and how harmful calls of "eat a [insert food of choice- cheeseburger, cookie, whatever]" are to your self esteem. I've known people who were ashamed of their thinness because people assumed they had eating disorders (but since when do people with eating disorders deserve to be mocked either, by the way?). Men ashamed of not being "manly" enough because they were very thin.
But here's the thing- it's just your body. Just the body that you were born with, that takes you through the day. Some of your bodies are healthy strong bodies and some aren't and that's okay too. At the end of the day it's a body that's completely and uniquely yours. You're the person who has to live with that body, so why not love it unconditionally and wholly? Whether thin or fat or anything in between your body is beautiful.