[BluffTHIS!]

Villain as described isn't the type of player most likely to be trying to push another tight player off a hand when OOP with a worse hand or draw. The reason the min checkraise is used by some is that with his stack it allows him to get the rest of his stack in on the turn without overbetting the pot. So fold 1 pair hands and call with draws and make him regret his raise amount when you hit a draw on him on the turn when he doesn't price you out of it (assumes your preflop raising range includes hands that could hit a draw here so you are not completely readable).