this hand is from a little while back, but I just started thinking about it again.

this was early in a hu match (a 6max table had just broken down), and pretty soon after i won a reraised pot vs him where i check-called down with top pair of aces vs his bluff. I don't think either of us have good reads, but generally view each other as pretty good tags capable of moves. he seems a little tighter pre flop then most tags though.
I checked behind the flop for pot control and to mix up my play. I know betting might be better, but I'm really looking for insights on the turn as the flop was played.

I'm not sure if he thinks I'd check behind a good one pair on the flop, but I did check-call that last time oop.

here is the hand...


Hand #39413214-7371 at Lincoln (No Limit Hold'em)
Started at 09/Feb/07 19:50:39

aegis9 is at seat 0 with $193.
Hero is at seat 5 with $326.30.
The button is at seat 5.

Hero posts the small blind of $1.
aegis9 posts the big blind of $2.

aegis9: -- --
Hero: :Kh:

Pre-flop:

Hero raises to $6. aegis9 calls.

Flop (board: Kd 4c 3d):

aegis9 checks. Hero checks.

Turn (board: :Kd: ):

aegis9 checks. Hero bets $12. aegis9 raises
to $48. Hero???
----------------------------------------------------------------

it felt weak (would he really check twice with a better hand on such a drawy turn?)...but I folded, figuring I'd be pretty clueless facing a big river bet almost no matter what card came and was not confident enough to 3bet.

What would you consider in this spot, and how would you play this turn and potential river bet?