As a side bar, I was told years ago that when Playgirl magazine was first published, men for the first time got to feel what it's been like for women forever it seems. (No one of either gender can compete with the perfect air-brushed bodies in magazines, etc., and many persons try so hard to look just the same as those pictures.)
I know this is a bit of an old thread, but I thought I'd add my thoughts.
I've gone out with a number of girls who have body image issues (my current girlfriend does). I don't think you can change the way she views herself, but you can be supportive and let her know that you find her attractive.
Saying "you're beautiful" might be rejected out of hand, but saying things like "you have beautiful eyes", or "I love your smile" might be accepted more.
Try not to go over the top, but make sure to give her enough complements so that she knows you find her attractive.
You should start working out (if you dont already) and encourage her to go with you. Start small. Eat healthier yourself and it will allow her to eat healthier too.
One thing you should do is when her mother or grandmother says something mean to her, stick up for her. Tell them (nicely) to shut the hell up. Make it vocal and public that shes beautiful.