Actually, that Weezing set will take 79.682928%-93.744621% from a +2 Life Orb Adamant Excadrill's Return, so it has a chance to 1HKO after 1 layer of Spikes. Realistically, you could call it an Excadrill check at best.
Also, using your favorites usually isn't going to get you far. When you play competitively, you do whatever you have to do to win as many battles as possible. There's a place for using your favorites, and that's in-game. Sure you feel better when you win using your favorites, but would you rather win with your favorites 1 out of 10 times, or win with the best team you could assemble 7 out of 10 times. If this was a gimmick team, I'd say use whatever you want. But this isn't, so if you want to be competitive with this team you really need to use the best Pokemon you have at your disposal.