50NL KK Makes Straight - But is it good?

[Cry Me A River]

Villain is a solid regular. 19.7/7.92/3.42 (500 hands).

PokerStars No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

UTG ($22.50)
Hero ($65.60)
MP1 ($51.90)
MP2 ($9.50)
MP3 ($32.30)
CO ($48.50)
Button ($9.25)
SB ($51.40)
BB ($45.05)

Preflop: Hero is UTG+1 with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/spade.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $2</font>, <font color="#666666">3 folds</font>, <font color="#CC3333">CO raises to $6</font>, <font color="#666666">3 folds</font>, Hero calls $4.

Flop: ($12.75) 9[img]/images/graemlins/club.gif[/img], T[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, CO checks.

Turn: ($12.75) J[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">CO bets $9</font>, Hero calls $9.

River: ($30.75) 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">CO bets $33.5 (All-In)</font>, Hero...???

Preflop: I am def NOT 4-betting this, only thing he calls/pushes with is AA. I want to see a flop and try to extract TT-QQ/AK.

Flop: Horible flop, only hands I'm beating are JJ/AK. His check is odd. If he has AK, he could be dodging my checkraise. Or he could have AA and be afraid that I'm the one with a set. I think he would bet QQ/TT/99 expecting a checraise from my AA/KK. No? I think he bets AA as well, wouldn't he?

Turn: Well, now it gets interesting - If he checked a whiffed AK he now has the nuts. OTOH, I'm beating everything else. I check/call to give him the opportunity to bet his set or AA, if he has it. Given the likelyhood that I'm the one with AK, his calling range has to be pretty narrow unless he just can't fold sets (I really don't have enough of a read one way or the other there).

River: I check again because I still have a hard time seeing him calling with anything I beat. Maybe I should block? He's obv raising AK but maybe not anything else, unless he reads it as a blocking bet. I have seriously under-repped my hand throughout. I'm hoping he makes it easy on me by checking it through or betting small but of course he pushes.

Can I call?