How far to push third nut

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Brick and Mortar $2-$4. The usual loose passives. No real reads on the villein. A quiet unassuming guy who kind of flies under the radar. This is a half kill ($3-$6) pot so to raise I have to throw $5 in. Not that this makes any difference.

I'm in the small blind with two black kings. Four limpers, I raise, BB reraises, two calls, I cap, everybody calls.

Flop is K [img]/images/graemlins/heart.gif[/img]-9 [img]/images/graemlins/spade.gif[/img]-4 [img]/images/graemlins/diamond.gif[/img]. I bet, everybody calls. Even tho I flopped the stone cold nuts on a drawless board, slow playing here would just cost me bets.

Turn is 9 [img]/images/graemlins/diamond.gif[/img]. I bet, villein in mid-position only caller.

River is A [img]/images/graemlins/diamond.gif[/img]. Unlimitted raising because we are heads up. I bet, he raises, I 3-bet, he 4-bets, I 5-bet, he 6-bets.

I think the river is the only street of interest. Correct me if I'm wrong.