2nd nuts on river vs nit...how much to bet?

[MrTimCaum]

2nd hour of the ftp $163. villain is like 12/5/2 over about 200 hands I have with him...the only hand I've seen him show down was early on in the 25/50. he came to the table with about 7k chips...3 limp in, sb completes, he checks QQ in the BB. flop was K53r checked around, turn was something like an 8, the SB bets 100, he calls, utg calls. river is a 7, sb checks, he checks, utg bets 300 and he calls, losing to 77. other than that, i haven't seen him show down anything.

now here's our hand:

Full Tilt Poker Game #1140284000: $22,000 Guarantee (7417839), Table 23 - 60/120 - No Limit Hold'em - 21:27:06 ET - 2006/10/23
Seat 1: Yankees31 (3,975) -SB
Seat 2: spike-hyzer (9,312) -BB
Seat 3: jaws2481 (3,630) - Villain
Seat 7: MrTimCaum (4,370) - me
Seat 8: boocks (2,165) - CO
Seat 9: NLBrewZ (7,810) - button
Yankees31 posts the small blind of 60
spike-hyzer posts the big blind of 120
The button is in seat #9
*** HOLE CARDS ***
Dealt to MrTimCaum [Q[img]/images/graemlins/club.gif[/img] Q[img]/images/graemlins/diamond.gif[/img]]
jaws2481 raises to 360
-3 folds-
MrTimCaum calls 360
-everyone else folds)
*** FLOP *** [J[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/spade.gif[/img]]
jaws2481 bets 480
MrTimCaum calls 480
*** TURN *** [J[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/spade.gif[/img]] [Q[img]/images/graemlins/spade.gif[/img]]
jaws2481 checks

-here I'm feeling like he's got AK or TT and is shutting down, so let's give him a look at the river and hope he improves.

MrTimCaum checks
*** RIVER *** [J[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/spade.gif[/img]] [5[img]/images/graemlins/diamond.gif[/img]]
jaws2481 checks

-ok, he's checked again, he's probably missed with AK or has a lower PP that has given up. what's the best bet to get value out of my hand here? pot size is 1860, he's got 2600ish left.

MrTimCaum?