NL 100: SC deepstack faces riverdecision

[CennyCripple]

SB is 19/15/3.4 over 100 hands. Has a river AF of zero

Button ($60.76)
SB ($359.15)
BB ($170.71)
UTG Hero ($218.97)

Preflop: Hero is UTG with 9[[img]/images/graemlins/spade.gif[/img]] 8[[img]/images/graemlins/spade.gif[/img]]
Hero raises to 4, 1 fold, SB raises to 12, 1 fold, Hero calls 8.50.

Flop (26.00) 6[[img]/images/graemlins/heart.gif[/img]] 8[[img]/images/graemlins/club.gif[/img]] Q[[img]/images/graemlins/heart.gif[/img]]
SB bets 20, Hero calls 20.

Turn (66.00) 7[[img]/images/graemlins/spade.gif[/img]]
SB checks, Hero bets 40, SB calls 40.

River (146.00) 4[[img]/images/graemlins/club.gif[/img]]
SB checks, Hero


Preflop is an easy call.

Flop I believe he's got AK, overpair or JJ. I call to float when hes got jacks and AK since I believe he will let go of it at turn if he doesn't hit. I don't thin he has QQ since he made a potbet with flopped set earlier on a drawy board. (not saying I'm right calling the flop but it probably looks a bit weird so I'm just trying to tell how I reasonated)

Turn I bet of course but since he calls I think he's got an overpair. I can't really see him have queens here. So the river brings a four and my intention was to shove all blank rivers.

But I got concered because of two reasons.
1. He might think he underrepresented he's overpair and might think he needs to call because of that.
2. Also he will prolly more often think that I might bluff pushing trying to represent a straight and that I would have checked down 2 pairs (would of course never do this but he might see me as a not so good player)

So do we push or do we check (and gives up the pot)
Will this type of player fold an overpair in this situation?

I have no read of him looking up bluffs or not.