Why don't you hand part of this over to an expert? Make an appointment for her with her doctor. This isn't the first such question your doctor has had. Let him/her explain to your girl about what being healthy is and how to think about weight. Doctors often have a way of doing that so that youngsters not only understand it but believe it! ("You're not fat" from a mama sometimes get a mental response of, "You're my mom and you have to say that.")
Your daughter's real problem, I suspect, is the girl/girls who call her fat. I wonder what they call other kids. You don't say that this other girl is a buddy, so I'm assuming that it's not a close friend. If I were your daughter's mama, I'd talk to her about why kids make the comments they do - and how they're usually not made out of love or friendship!
(I'd also take her with me next time I went shopping and point out ALL the ski coats - showing how they don't make anybody look good.)
She needs to know that this sort of people-trashing is nothing but a power game; if you say something to me to make me feel bad, and it does make me feel bad, then you have power over me and you feel more like a Somebody. It's a pathetic way to feel like a Somebody!
Your daughter does not have to take seriously any comment like that; in fact, if she could come up with some sort of standard reply (like, "Thank you for your information"), she might feel more equipped to handle such barbs and might even be able to help others handle the same sort of words.
She also needs to know that any teasing or bullying is something Mom and Dad need to hear about, because it means there's a problem. No, she's not the problem. It's something going on at the school.
It's too bad that eight-year-olds have to learn emotional defenses along with arithmetic and spelling, but that's the sort of planet we live in.