draw three souls out of one weaver Sir Toby alludes to two common ideas of the time:

1. Music can draw the soul out of the body.
2. Weavers are pious psalm-singers who hate ungodly music, such as a catch.

So, if the catch can "draw three souls out of one weaver," it will be the best catch ever.

Why "three souls"? Maybe because the three singers—Sir Toby, Sir Andrew, and the Clown—will each be able to draw one soul. Or maybe because one soul has three aspects: vegetal, sensible, and intellectual. Or maybe just because Sir Toby is drunk.