Definitely should have raised pre-flop. That goes without saying.

I smell some desperation on the part of the short stack. I think if his hand was truly a monster, he would have smooth called the $3 raise to try to keep the other players in the hand. Maybe a drawing hand, but possibly two pair, or top pair. I think given the size of the pot and the size of the bet, you make the call and find out. You would not have to face any future bets by this opponent, and you may have been winning at that moment.