3/6 - Value bet this river with KK?

[ChicagoPoker]

I figured after he checked the turn my hand was good. Then the river came. I figured he had an A here because of his 3bet pf. So I guess my question is, is value-betting this river justified? I'm probably only beating TT-QQ right?

Villain was 29/18/2 over ~50 hands...

Full Tilt 3/6 Hold'em (4 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Preflop: Hero is UTG with K[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/club.gif[/img].
<font color="#CC3333">Hero raises</font>, Button calls, <font color="#666666">1 fold</font>, BB calls.

Flop: (6.50 SB) 4[img]/images/graemlins/club.gif[/img], 9[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, Button folds, <font color="#CC3333">BB raises</font>, <font color="#CC3333">Hero 3-bets</font>, BB calls.

Turn: (6.75 BB) 7[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, BB calls.

River: (8.75 BB) A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, Hero ????