Weedle, Kakuna & Beedrill (it's 3 forms) will need a lot of help until it reaches level 20, when it learns Beedrill's signature move - Twineedle.
Once that move is learned, you'll find that it can become a power-house for dealing with Grass, Psychic & poison type Pokemon ingame.
Personally, I always enjoy using a Beedrill - regardless of which generation's game I'm playing. Just don't expect it to cope well competitively against other players. Not only does Beedrill need time to set up in order to battle competitively, it also needs a little bit of luck in it's favour. For ingame, however, you could easily solo the game with Beedrill once Twineedle's learned.
Where logic won't work - I will PAL Gamers unite - http://www.gamefaqs.com/boards/277-pal-gaming