I don't think it's gonna happen. Maybe if there is a demand for fatties they start making anime with 'token fat girl'.
I see some big problems, though. If you're big, you can't be small and cute. Second, getting fat is something that usually happens when you stop growing (implying 20+). Also, if it is not a disease (I don't believe fatness could replace 'weak constitution' etc. as the sickness sick girls have) it is caused by eating a lot. I agree eating is cute, but if it's your favourite past-time it makes you seem dull.
Then again, there are fish.