I think you're stretching the definition of "stereotypical black caricature." Initially, you think he's the wisecracking sidekick, but he's buff and shows he can take care of himself, and then he gets the girl. The WHITE girl. I think they did an ok job busting what looked like a standard-issue secondary minority character in that first film.
As for this movie... whatever. Hollywood pushes so many genres past their natural breaking point these days that there's no reason to parody them, since they have built-in post-modernist concepts and self-referential gags and ideas.