Stars 2/4--TPTK against likely draw

[WordWhiz]

PokerStars 2/4 Hold'em (10 handed)

Villain is solid, 2+2'er.

converter

Preflop: Hero is BB with A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img].
<font color="#666666">6 folds</font>, Villain calls, Button calls, SB completes, <font color="#CC3333">Hero raises</font>, Villain calls, Button calls, SB folds.

Flop: (7 SB) K[img]/images/graemlins/spade.gif[/img], 7[img]/images/graemlins/diamond.gif[/img], 9[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">Villain raises</font>, Button folds, <font color="#CC3333">Hero 3-bets</font>, Villain calls.

Turn: (6.50 BB) J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, Villain calls.

River: (8.50 BB) 6[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Villain bets</font>, Hero ???

Final Pot: 8.50 BB

Thoughts? How many of you would call here? How often do you think you're good if you do?

BTW, DON'T TELL ME I SHOULD HAVE BET THE RIVER RATHER THAN CHECKING.

I know that. In fact, this isn't exactly how the hand went down. This is a bit of a thought experiment. I can't say too much without giving away the secret, but I'll post a revised HH and ask for further comments if I gather enough interest here.