25NL:QQ against station who checks nuts on river twice...180bb deep

[meccaNES]

Ok after taking me some shots and doing like [censored] i cashed out and am bankroll knitting my way up. Anyway...

Villain is 40.2/3/.54 I've seen him check the nuts TWICE on the river...

How deep deep do you have to be before valuebetting can become dangerous?

We're what ~ 180bb deep? Am i missing a [censored] ton of value here by not just shoving the river? It's like 22 into a 40$ pot. I think he calls with any jack. But, since he's been calling since the flop he may have rivered the 7 or a busted flush.

Exactly how deep can you go with one pair against a station who also checks the nuts on the river? This question is probably more important than the actual hand.

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

BB ($26.20)
UTG ($44.85)
MP ($20.45)
CO ($31.45)
Hero ($42.40)
SB ($24.75)

Preflop: Hero is Button with Q[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/diamond.gif[/img].
UTG calls $0.25, <font color="#666666">1 fold</font>, CO calls $0.25, <font color="#CC3333">Hero raises to $1.75</font>, SB calls $1.65, <font color="#666666">1 fold</font>, UTG calls $1.50, CO calls $1.50.

Flop: ($7.25) J[img]/images/graemlins/club.gif[/img], 7[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, UTG checks, CO checks, <font color="#CC3333">Hero bets $4.25</font>, SB folds, UTG calls $4.25, CO folds.

Turn: ($15.75) 9[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
UTG checks, <font color="#CC3333">Hero bets $13.5</font>, UTG calls $13.50.

River: ($42.75) 7[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
UTG checks, <font color="#CC3333">Hero ? Instashoves or checks behind on the slim chance he isn't ahead...?

This seems kind of stupid since i just reread it...