There’s a big issue with using weight classes in team sports: player weights vary dramatically. Take the NFL for example. Setting aside the enormous differences in weight between linemen (offensive and defensive) and all other position players, there are also huge weight differences within a given position. For example, quarterback Jared Lorenzen was 6’4” and weighed 275 lbs whereas Russell Wilson is 5’11” and weighs 211 lbs. That’s a huge weight difference!
You can find similar weight differences across players in other leagues (NHL, NBA, and MLB). Weights don’t really correlate with overall skill level though they do somewhat correlate with position and skill set (and height of course).
How would you classify by weight in team sports? You might think to do it by position but none of the leagues require a player to remain at a single position for their career. Players can and do switch positions, and many even do so multiple times during a game. Sports like NBA basketball don’t even have any particular rules about what a player at any given position is allowed/not allowed to do, so the positions on team rosters are more like a suggestion than a requirement.