River: c/r or b/r ?

[HoneyBadger]

Villain is quite solid, a tad passive (2.0), but overall a good player (over 5k hands)

Preflop: Hero is UTG with J[img]/images/graemlins/spade.gif[/img], J[img]/images/graemlins/heart.gif[/img].
<font color="#CC3333">Hero raises</font>, <font color="#666666">6 folds</font>, <font color="#CC3333">Button 3-bets</font>, <font color="#666666">2 folds</font>, Hero calls.

I don't cap here because I'm OOP; villain is good; knows I am; hence, I don't like JJ that much.

Flop: (7.50 SB) 8[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 9[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets</font>, <font color="#CC3333">Hero raises</font>, Button calls.

Overpair, standard c/r in my book. I c/r draws here, so I must balance my range by c/r-ing overpairs

Turn: (5.75 BB) 3[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">Button raises</font>, Hero calls.

I must bet here. Ok, he went for a call c/r, raise turn line. He knows I'll bet the turn no matter what after the c/r.So he probably either has AK here he wants to take to a free showdown, or a better overpair; the latter being more likely, so I go into call-down mode.

River: (9.75 BB) J[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>

Jackpot, I have him beat. How to extract the most? I'm almost 100% certain he will bet if I check and call my raise; however, would he raise me if I bet out? Will he see this as some weird wa/wb line and raise QQ+? Maybe even AK as a bluff? Or is a c/r better, knowing he will bet out?