LOL. That is so funny. How the hell can you say something like that ? HAHAHA

It is not only the fact that you say that she is fat. You immediately show your interest. Basically you said that she is fat but you still want to date her. She must get the feeling that she earned a date with you, not that you earned a date with her. People want what they can't have or what they get with difficulty. If something comes too easy, they don't want it. I know a guy that is known to hit on ugly girls only because they are easy. I can tell you that all girls that know this guy consider it as a disgrace to get hit on by him. If there is 1 guy in the world they would never want to date, it is him. So don't even bother anymore with this girl, you screwed this one over, big time. Instead, go out with her to parties and use her as a pawn in order to attract other females that are better than her. If she sees this, she might get a different view of you and feel attraction for you.
I do agree that it is difficult to say something to a girl when she is complaining that she is overweight. If you make a cocky funny statement you can insult her. Probably she comes up with this subject because she wants you to make her feel better. She wants you to say: "But no, you are not fat. You are just perfect like this.". Therefore, the best thing you can do is frame control and just ignore that comment. Just switch the topic.