KK - HU when Ace flops

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Party Poker 2/4 Hold'em (8 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Preflop: Hero is UTG with K/images/graemlins/club.gif, K/images/graemlins/spade.gif. MP2 posts a blind of $2.
<font color="CC3333">Hero raises</font>, <font color="666666">6 folds</font>, BB calls,

Flop: (5.50 SB) 3/images/graemlins/diamond.gif, A/images/graemlins/diamond.gif, 3/images/graemlins/club.gif <font color="blue">(2 players)</font>
BB checks, Hero checks.

Turn: (2.75 BB) J/images/graemlins/heart.gif <font color="blue">(2 players)</font>
BB checks, <font color="CC3333">Hero bets</font>, BB calls.

River: (4.75 BB) 9/images/graemlins/spade.gif <font color="blue">(2 players)</font>
BB checks, <font color="CC3333">Hero bets</font>, BB calls.

Final Pot: 6.75 BB
<font color="green">Main Pot: 6.75 BB, between BB and Hero.</font>

What do you think of this hand, in particular my check on the flop. I can't lay KK down heads-up vs. a calling BB with almost any flop. I figure I'm either way ahead or way behind on a flop with an ace so I decided to check, and entice my opponent to call me down if he does hit the board on the turn. I figure I'll save 1 SB the times I'm up against an Ace, and gain sometimes 2 extra BB the times I winning.
I do think this play would only work against weaker opponents, but this is for small stakes.

Thoughts?

[papawawa]

yeah, but if he is in fact drawing, don't you want to charge him for the free card?

[MoreWineII]

I would have bet the flop, I think. I don't give a HU opponent credit for an ace by default.

Once he checked the turn, I would have bet out for sure.

Looks like you have a pretty passive opponent there.