blind defense--scary river

I figure I should learn how to post a hand one of these days, so here goes:

CO is 28/22/2.3, Button is unknown.

Party Poker 3/6 Hold'em (6 max, 6 handed) FTR converter on zerodivide.cx

Preflop: Hero is BB with K[img]/images/graemlins/heart.gif[/img], 9[img]/images/graemlins/spade.gif[/img].
<font color="#666666">2 folds</font>, <font color="#CC3333">CO raises</font>, Button calls, <font color="#666666">1 fold</font>, Hero calls.

Flop: (6.33 SB) 4[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
Hero checks, CO checks, <font color="#CC3333">Button bets</font>, <font color="#CC3333">Hero raises</font>, CO folds, Button calls.

Turn: (5.16 BB) 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, Button calls.

River: (7.16 BB) A[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks

I c/r the flop because that's what I do in the BB. I don't want to either call or fold to a river raise, so I figured that I would check/call. Should I be bet/folding? I don't see what worse hands will call as my play screams out that I have a naked king or maybe 44 or 66.