I think most of what everyone has said here is true.

As far as why people say stuff like that, yea women say it because they hate on skinny girls out of jealousy or resentment, alot of guys say it cuz they sincerely like thicker women...

But I think alot of guys say that nowadays just because they think its what girls want to hear, they say it to score brownie points. Because alot if not most women hate on skinny women, and not many women consider themselves skinny, even the skinny ones, so when a guy says he doesn't like skinny women, he likes them bigger, he's trying to slip in a backdoor compliment to the girls who don't consider themselves skinny, and make them feel at ease about their bodies. Basically they're just flirting.

The vice versa is when girls say they like geeky guys, it may or may not be true but they're mostly just flirting, to put guys at ease about acting cool. Or alot of girls who watch sports but really don't care about them, again they're just saying they like whatever they think the opposite sex wants to hear.