So, in conjunction with that, make weapons limited by Str. One suggestion in another thread was:
Str <12 D4 weapons
Str 13-14 D6 weapons
Str 15-16 D8 weapons
Str 17-18 D10 weapons
etc
This means a fighter with 17 Str, for example, would be willing to use any d10 weapon he can get his hands on...