KK, 4-bet PF, 3-bet flop and turn on J-high...

I know I'm posting a lot of these today... but I feel like I'm playing poorly and want some advice.

No reads on the BB yet.

Party Poker 0.50/1 Hold'em (9 handed) converter

Preflop: Hero is MP2 with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/club.gif[/img]. CO posts a blind of $0.50.
<font color="#666666">3 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">2 folds</font>, Button calls, <font color="#666666">1 fold</font>, <font color="#CC3333">BB 3-bets</font>, <font color="#CC3333">Hero caps</font>, Button calls, BB calls.

Flop: (13.50 SB) 5[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">BB bets</font>, <font color="#CC3333">Hero raises</font>, Button calls, <font color="#CC3333">BB 3-bets</font>, Hero calls, Button calls.

Turn: (11.25 BB) 9[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">BB bets</font>, <font color="#CC3333">Hero raises</font>, Button calls, <font color="#CC3333">BB 3-bets</font>, Hero calls, Button calls.

River: (20.25 BB) 4[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">BB bets</font>, Hero calls, Button folds.

Final Pot: 22.25 BB

Before the flop I knew if any card T+ other than a K came up, I might be against trips. That or AK.

On the flop, should I have capped? I knew I was only ahead of QQ and AK (with a spade in there probably). I doubt he would re-raise with TT here.

The turn... once again I thought I might be trailing already. When he re-raised me again, I just called down. Not much more I could do. He wouldn't lay off the aggression and he could have aces or trip jacks already.

I'm thinking I was too aggressive on the turn and should have capped the flop instead.

Any advice?