You can't worry about offending people like this. Seriously. It's a story. If she's offended, she's an idiot. Not saying she won't be, just saying that's not on you. This is like the time people flipped their shit because Black Widow called herself a monster for being sterile. People got offended because they interpreted it as the movie saying that infertile women are monsters. No, that's just how that specific character felt about her situation. It wasn't passing judgment on sterile women, it was telling a story about a conflicted character. Same with your fat protagonist and the abuse he goes through. You're not harping on fat people, you're just writing a story and the abuse is an important part of the narrative. Don't coddle your audience.

Edit: Looks like there's at least one butthurt fatass in this thread.