What's going on here?

[Sushiglutton]

Reads: Villain is 27.9/16.4/2.3. I have seen him overplay a couple of hands. He 3-bet A9s agaisnt an early raiser and lost to AJo cold-calling 3 behind him (yes, this game is beatable...). In an other hand he overplayed AK agaisnt a cold-caller, 3-bet turn and donk call river on a 445Kx board after his villain capped the turn.

What's going on here? On the flop I thought about checking, but decided that 3-handed and with my BDDs it was worth a shot. On the turn I picked up some clean outs and thought he could very well pull the trigger again. And now giving FC isn't scary at all, so I think it's a clear check. On the river he thinks for almost 30 secs and then check. Is that to scare me to check, or invite me to bet? And what should I do?

PokerStars 0.50/1.00 Hold'em (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Preflop: Hero is Button with A[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/heart.gif[/img].
UTG calls, <font color="#666666">5 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">BB 3-bets</font>, UTG calls, Hero calls.

Flop: (9.50 SB) 3[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, UTG checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">BB raises</font>, UTG folds, Hero calls.

Turn: (6.75 BB) K[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, Hero checks.

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