A9o mp on monotone board

[dave44]

Villain is 45/17/1.7 after only 60 hands.

Party Poker 10/20 Hold'em (6 max, 6 handed) converter

Preflop: Hero is UTG with A[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/club.gif[/img].
<font color="#CC3333">Hero raises</font>, <font color="#666666">4 folds</font>, <font color="#CC3333">BB 3-bets</font>, Hero calls.

Flop: (6.50 SB) 6[img]/images/graemlins/heart.gif[/img], 9[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, Hero ?

What's my line here? I'm leaning toward the passive side, check-calling the flop and turn thinking that a heart isn't going anywhere and may even knock me off the best hand and if I am ahead he probably has something like AQ which only has 3 outs.