Really Confusing Line By Villain

From a 180 SnG on Stars. I've opened very few pots so far, showing down only KK and AA. I (correctly) called a large all-in over my continuation bet on an 89J flop when I had KK, the AA was all-in pre-flop. The only other pot I played so far I won without a showdown out of the the BB. No reads on Villain.

PokerStars No-Limit Hold'em Tourney, Big Blind is t50 (8 handed) converter

BB (t2535)
UTG (t5560)
UTG+1 (t2170)
MP1 (t1675)
Hero (t6070)
CO (t2930)
Button (t3717)
SB (t2595)

Preflop: Hero is MP2 with J[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/club.gif[/img].
<font color="#666666">3 folds</font>, <font color="#CC3333">Hero raises to t150</font>, <font color="#666666">2 folds</font>, SB calls t125, <font color="#666666">1 fold</font>.

Flop: (t350) J[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets t200</font>, <font color="#CC3333">Hero raises to t600</font>, SB calls t400.

Turn: (t1550) A[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

River: (t1550) K[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets t650</font>, Hero folds.

Final Pot: t2200

His line here really confused me. I didn't think he would lead out a K on the flop, so I thought either a set, a J, or QT was most likely. My raise was mostly to find out where I stand and put me in control on the turn- I was planning on folding to a push.

The A on the turn is a mixed bag. I'm now ahead of KJ, but I don't think that's among his more likely holdings. If he had QT or a set, then this is actually a trap card for me. I check behind to keep the pot small.

The river K pretty much seals it for me, I think- hard to see what I'm ahead of at this point. I don't like folding when I can't put Villain on a particular hand, but here I think I'm way behind his range. What do you put him on? What do you think of my line?