AK in the small blind v. short stack

[Rococo]

2-4 NLH, 8 handed, I have approximately $320. Villain is extremely short stacked at $95. Stack sizes for other players are between $150 and $300. I am fairly new to the table but it seems extremely loose passive before the flop.

Preflop

4 players limp in, including the Villain on the Button. I make it $20 to go in the SB with A [img]/images/graemlins/heart.gif[/img]K [img]/images/graemlins/diamond.gif[/img]. All fold to the Villain on the Button, who calls.

Flop: T [img]/images/graemlins/club.gif[/img]7 [img]/images/graemlins/spade.gif[/img]2 [img]/images/graemlins/diamond.gif[/img]. I bet $40 hoping to take it down right there. Button calls. Not good. He now has $33 left in front of him.

Turn: 4 [img]/images/graemlins/heart.gif[/img]

I check to the Villain. He checks behind.

River: 4 [img]/images/graemlins/spade.gif[/img]

I check to the Villain. He checks behind. ????

Unsure of play on virtually every street. No real draws on board, so I assumed that I was behind after he called a sizeable bet on the flop. Because of his short stack, my gut told me that he would call a bet on the turn or the river with virtually any hand that I could put him on.

Comments welcome.