How'd I play those overcards?

[AngelicPenguin]

Villain (mp3) had been loose and aggressive postflop through 40 or so hands. I had no other notes on him other than "Lag?" His numbers were 47/7/4.0.
BB was VERY passive. Having not bet or raised an overpair (QQ) on an earlier hand. He was also playing about half his hands with no raises at all over about 40 hands.

Party Poker 0.50/1 Hold'em (10 handed) converter

Preflop: Hero is UTG+2 with K[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/club.gif[/img].
<font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">2 folds</font>, MP3 calls, <font color="#666666">3 folds</font>, BB calls.

Flop: (6.50 SB) 2[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, MP3 calls, BB calls.

Turn: (4.75 BB) Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, MP3 calls, BB folds.

Since BB checked, I figured I had a shot of losing him.

River: (6.75 BB) J[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, MP3 calls.

With only one loose player who had played reasonably aggressive with his hands, I figured I might have him beat here. Am I only getting called by hands that beat me, so a check/call is in order?

Final Pot: 8.75 BB