True, true, it's mostly that the author seems to be going to great effort to make small kang look bad, not that his being heavy set automatically makes him that way..........and yeah, she's also being portrayed as pretty darned stiff and picky too. In all fairness though she probably can't help herself, she's apparently lived a sheltered life of privilege and doesn't know any other way to be.
It makes sense for the author to put a lot of emphasis on making the small one look bad.
You have to remember that this is in korea. Being overweight in asian countries like Japan or Korea isn't perceived the same way than, in let say, North America. It's a lot more stigmatized. He's fat, weak, and pretty slow up there too. Overall not someone you'd want to hang out or live with.
It's true that she's stiff and picky because she's been sheltered. But I'm sure that's more because she has always been alone. Grandpa probably is a workaholic and ... the parents. I forgot, but they don't look like they're around, did they die the cliché death of some airplane/car crash accident? I can't seem to remember if that's the case.
If you live alone a lot you tend to not be able to cope with the fact that others have different values or likes/dislikes then you.
Especially if they're of different sex, doubly true when in context of countries that separates gender a lot in terms of live choices and obligations.