Is this play +ev?

[DiceyPlay]

Opponent is 8.5/4.25/12.5 after 94 hands

My thinking pre-flop is I've got an ace, let's see the flop for one small bet closing the action.

My thinking on the turn is he could have AA 3 ways, KK 3 ways, AK 9 ways.

Paradise Poker 1/2 Hold'em (10 handed) converter

Preflop: Hero is BB with A[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/club.gif[/img].
<font color="#666666">3 folds</font>, <font color="#CC3333">MP1 raises</font>, <font color="#666666">1 fold</font>, MP3 calls, <font color="#666666">3 folds</font>, Hero calls.

Flop: (6.50 SB) 9[img]/images/graemlins/diamond.gif[/img], 9[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
Hero checks, <font color="#CC3333">MP1 bets</font>, MP3 folds, Hero calls.

Turn: (4.25 BB) K[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">MP1 bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">MP1 3-bets</font>, <font color="#CC3333">Hero caps</font>, MP1 calls.

River: (12.25 BB) 4[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">MP1 raises</font>, Hero calls.

Final Pot: 16.25 BB

Results in white below: <font color="#FFFFFF">
Hero has As 9c (three of a kind, nines).
MP1 has Kh Ks (full house, kings full of nines).
Outcome: MP1 wins 16.25 BB. </font>

I think capping the turn costs me three extra bets. Do I normally win two extra bets instead of losing three?

Should I have not waited until the turn to cr? He's not going to lay down KK on the flop. He'll probably go into call-it-down mode until he hits his K on the turn -- right? Should I have slowed down on the turn when he 3 bet? I think AK was very likely at that point and he would have bet it that way too -- no?

All comments appreciated.

-DP