Is this a good time to check behind?

[GoCubsGo]

PokerStars No-Limit Hold'em, $0.02 BB (9 handed) converter

MP3 ($5.43)
CO ($5.01)
Hero ($5.43)
SB ($3.23)
BB ($6.07)
UTG ($1.78)
UTG+1 ($2.28)
MP1 ($1.71)
MP2 ($5.37)

Preflop: Hero is Button with K[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">UTG+1 raises to $0.09</font>, <font color="#666666">3 folds</font>, CO calls $0.09, <font color="#CC3333">Hero raises to $0.18</font>, SB calls $0.17, <font color="#666666">1 fold</font>, UTG+1 calls $0.09, CO calls $0.09.

Flop: ($0.74) 5[img]/images/graemlins/spade.gif[/img], 2[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, UTG+1 checks, CO checks, <font color="#CC3333">Hero bets $0.5</font>, SB calls $0.50, UTG+1 folds, CO folds.

Turn: ($1.74) 5[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets $0.8</font>, SB calls $0.80.

River: ($3.34) Q[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

Final Pot: $3.34

I see a lot of strong hands check call flop, check call turn, and check raise the river. I thought there was a decent chance he had AA. I didn't think of it at the time, but he could have also had QQ and hit his set. I don't think I could call if he raised my bet. On the other hand, he could have had an ace and was chasing the 4. 66-JJ are also decent possibilities. I don't think he calls a bet with many hands that I have beat. Is a check on the river too weak?