I would side with saying the reader has to be discerning. In the case of this piece, it's the reader's job to finish the whole story and the writer's job to make it clear she is writing a fat, slobby character who -- as the opening paragraph -- is meant to convey exaggeration and hyperbole. Ultimately, if it's not overdone and is, in fact, satire--the character should be contextually appropriate and not offensive. Then again...becoming offended is sort of de riguer these days.