Flopped Set - When to slow down

[Paxosmotic]

I played this hand tonight and thought it would be interesting to see when you'd slow down with a flopped set. I have 949 hands on Villain at this level. He's 19.18/10.54/2.31. He's an attractive and thinking TAG who seems to be playing well below his bankroll and is consistently outplaying the table. Villain seems to have an advanced knowledge of poker theory and is very good at putting his opponents on a hand, as well as finding good opportunities to bluff. All in all, Villain might be the greatest 1/2 player in the history of... alright, it's me. I am the Villain in this hand. From Hero's perspective, when do you slow down here? Also, what does Villain have?

PokerStars Hold'em (9 handed)converter

Preflop:Hero is UTG with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/spade.gif[/img].
<font color="#CC3333">Hero raises</font>, <font color="#CC3333">Villain 3-bets</font>, <font color="#666666">3 folds</font>, CO calls, <font color="#666666">3 folds</font>, <font color="#CC3333">Hero caps</font>, Villain calls, CO calls.

Flop: (13.50 SB) A[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/heart.gif[/img], 8[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">Villain raises</font>, CO calls, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">Villain caps</font>, CO calls, Hero calls.

Turn: (12.75 BB) 5[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">Villain raises</font>, CO calls, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">Villain caps</font>, CO calls, Hero calls.

River: (24.75 BB) Q[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">Villain raises</font>, CO folds, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">Villain caps</font>, Hero calls.

<font color="white">I bet/call the turn and check/call the river. </font> &lt;- My answer.