She is worried that if she is fat, will you still love and hate her?
As long as you tell her that she is fat, you will love her as much as you do, or love her more, and she will feel at ease and can eat with confidence. What she wants to hear is your promise.
Of course, if she is really fat, do you still love her or not, and will you hate her? That was your problem. This has never happened, who knows.