(Note: This is not valid in all cases. Sometimes "spoiling" a girl is just fun, or romantic, if you want, so don't take this too serious, and girls: I hope you will not be offended - If you are please /msg me and tell me why.)
I'm currently in my fourth year in boarding schools, and I hear these kinds of comments or questions all the time. They come from all kinds of girls, but what they want is basically the same thing: They need you to tell them that they are wrong, that they are the most beautiful girl in the world, or that they have the most beautiful eyes in the universe, etc. etc.. So I have been asking myself - Should I really keep telling what they want to hear, complimenting them all the time in an eternal meaningless game?
Sure, in many cases girls are just "down", and compliments and nice words help them feel better, just like boys \ men. In a few cases however, I have noticed that girls (Yes, this probably goes for men too, but I have not seen it - at least not nearly as often as with girls) become complete complimentoholics - If you don't give them a compliment every half hour they start whining about how fat they are, or how ugly they are, or about the girl who lives down the corridor and is so beautiful that all the boys want her, blah-blah-blah - I can't believe I'm supposed to keep this going?
If girls are like this, often they will simply be overlooked after a while. They will start whining about everything and anything, just to get some attention, to see if anybody cares. Other people will get even more tired and annoyed with her. Now if one or two people start being nice to her and give her compliments, what happens? She starts hanging around with these guys, and they can never get her of their back, and they have to keep complimenting her for ever. If they don't, she will be completely PISSED OFF, claiming they treat her badly and that they are bad friends.
What I'm saying is that girls are often easily spoiled - not (only :) ) by money, but by compliments. So what is my opinion on what you should do if a female should suddenly decide to lay all her weight-problems on your humble shoulders?
Avoid the question.
Try somehow to give an excuse not to answer. This can be hard, because she will start whining and complaining that you think she IS fat, and that you are embarrassed by her. After a little denying, you can now admit that she is indeed NOT fat, but that you just hate answering such questions, simply because it puts people in lists. It puts some people above others in an unfair way, and doing this gives you a bad conscience. (True for my sake at least!)
Now tell her that you love her or are fond of her as a friend or whatever anyway, no matter what she looks like, etc. The trick is to be able to tell her you like her without starting that hopeless fake compliment-act (Which she probably knows if a play anyway; As Demeter said: What she really is asking is Do you love me?. Tell it to her in an honest and real way.