I'd bet. The check seems suspicious. If you called the $6 and he had a hand that he wanted action with, he'd have (or at least should have) raised the turn.
I'm pretty sure that he has a a flush draw. Maybe the Ace of spades, and a non-King face card. As/Qx? As/Js? As/Tx maybe if he's loose (because he raised UTG).
Assuming he's drawing with two overs, one being a spade, it's pretty much a coin flip on the flop. In fact, he was a slight favorite. But that 3h on the turn wasn't likely to help him, and cut his odds
of winning in half. So now you're the big favorite.
He has $16 left and the pot is $24, right?
Shove. Then pray you're the 2/1 favorite.
Then scream and tear your hair out when he shows his slow-played K/9.