Villain is 33/14/2.5 over 114 hands

Full Tilt Poker $0.10/$0.25 No Limit Hold'em - 8 players - View hand 31178
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SB: $18.35
BB: $15.55
UTG: $15.35
UTG+1: $20.80
Hero (MP1): $34.50
MP2: $40.35
CO: $16.45
BTN: $12.65

Pre Flop: ($0.35) Hero is MP1 with K K
1 fold, UTG+1 calls $0.25, Hero raises to $1.25, 5 folds, UTG+1 calls $1

Flop: ($2.85) 4 8 9 (2 players)
UTG+1 bets $2.85, Hero raises to $8, UTG+1 calls $5.15

Turn: ($18.85) A (2 players)
UTG+1 checks ???

What should I put him on here? Do I shove and hope he's on a draw not containing the As? Do draws call or just hands that beat me?

Check behind. Your hand, which the second nuts pf has devolved down to a bluff catcher. He made a pot sized donk bet (PSDB), which means he's just as worried about the FD as you are. He's possibly worried that you have AA and just beat his lower set. However, he isn't going to be worried enough to fold to your bet if he has a set. By checking, you set up the possibility that you raised with your FD and overs. If the spade comes on the river and the villain checks, I'd make a PSB on the river. If it doesn't and he makes a big bet, you'll have a hard decision. Since I'm in a 12 step program to stop calling big bets on the river with over pairs, I'd fold, but others who aren't doomswitched might advise otherwise.

So, I feel like if I check behind he knows I don't have an A. So, he can push as a bluff or with a good hand and I'm stuck guessing.

Tough spot, villain doesn't have much of a stack left. So really any bet he goes all in and how do you fold getting better than 2.5 to 1 against a donk if he bets a non flush river? I think when you raise the flop you're pretty much committed given his stack size. Bet turn or Check and call non spade river and pray its TT-JJ or a draw. I think I prefer checking the turn. You get more of villains range that way.