If this guy is a fish, I can mimic his thinking with disturbing ease. I reckon he has TPNK until the river, which scares the crap out of him, so he bets hoping you'll just call, because if he checks he knows you'll bet more than he wants to call. Even though he would call anyway. Alternatively Kx spades would keep him interested, and he was looking for a raise on the river. I'm guessing here based on how I'd have played those hands a few months ago.

At any rate, I agree that if you're going to win this pot, you won't be getting any more of his chips into it.