AA - river value bet or check behind?

[Genesis]

SB has been here for about 5 hands. I think he's seen 4 flops out of 5. Last hand I opened from Button, he called to river on 876Q6 board before folding.

Button sees nearly 100% of flops. Will call flop with any draw, any pair. Passive.

SB $7.75
Hero $12
Button $30
10NL 6max

Hero opens A [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/club.gif[/img] for $.35, Button calls, SB calls.

Flop ($1.15)
K [img]/images/graemlins/spade.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img] T [img]/images/graemlins/spade.gif[/img]
SB checks, Hero bets $1.15, Button folds, SB calls.

Turn ($3.45)
J [img]/images/graemlins/heart.gif[/img]
SB checks, Hero bets $2.25, SB calls.

River ($7.95)
4 [img]/images/graemlins/club.gif[/img]
SB checks, Hero...

Ok, SB has about $4 left. Is this an obvious time to put him all-in, or should I consider checking behind here?