OP, let's face it, you're a jerk either way. If you break up with her now, she knows it's because she's fat. But if you don't, you're just fooling yourself, and her.

She obviously doesn't want to break up with you. It frustrates me to say this, but I don't think she has much respect for herself.
I just don't think it's healthy, this type of relationship that you have, with you being able to mould her. If you told her to lose weight, I'm sure she would, just to keep your affection. But that's what worries me.