That's really obnoxious. Two of my best friends are fat. I have a fat cat and I know she probably won't make it through the end of my college life. I think the fat shaming here was just a cop-out. She saw you needed an explanation and she gave you one. It was total bs but it seemed to satisfy you. It's like me telling my friend's mom that she can't find a boyfriend because she's blonde and he's worried that their children would turn out to be stupid (for lack of a better word; sorry, guys, I just woke up).

Maybe it's just me, but I find skinnier people less approachable than fat people (I find almost everyone unapproachable actually).