Its funny. I think if you took away the context of it being an old Shakespeare play, most people would find The Taming of the Shrew (which 10 Things I Hate About You is very loosely based on) fairly abhorrent.
The Merchant of Venice is blatantly anti-Semetic. The Comedy of Errors has a whole scene that's just fat shaming for no good reason. There's plenty of other examples of things that would be problematic if written in a modern context. Obviously it wasn't problematic several hundred years ago, and we shouldn't judge Shakespeare by modern standards.
I really don't think fat jokes are considered off-limits for present-day comedies.