I think she's saying that it's the perception of fat that's a social construct, and I agree with that to an extent.
For example, I saw a segment from a talk show about an African man who put on more than 50kg (110lbs) after he moved to Australia. His family back at home was really happy for him. You'd probably find similar attitudes in other parts of the developing world, where a lot of labour is still done manually, living standards are low, therefore being fat is a sign of prosperity.
However, that has nothing to do with what Virgie's talking about. Like every Fat Acceptance lolcow who flaunts her body like it's the hottest thing ever, Virgie never got over her middle school butthurt-ness over the fact that other girls are prettier, thinner and more popular than she is. Fat Acceptance (more like Fat Evangelism) is her way to get even, by arbitrarily redefining 'beautiful' so that she is now at the top of the pecking order and those skinny bitches are at the bottom.
It's one level of stupid that Virgie and her ilk never put any serious, disciplined effort into becoming thin and popular like they obviously want to be. It's orders of magnitude more stupid that they believe having hordes of admirers drooling over their bodies is the best and only marker of success in life.