AQs 2nd pair vs. cap

[dave44]

Villain is 36/20 over 19 hands or just unknown.

Party Poker 10/20 Hold'em (6 max, 6 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Preflop: Hero is BB with A/images/graemlins/club.gif, Q/images/graemlins/club.gif.
<font color="#666666">1 fold</font>, <font color="#CC3333">MP raises</font>, <font color="#666666">1 fold</font>, Button calls, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">MP caps</font>, Button folds, Hero calls.

Flop: (10.50 SB) Q/images/graemlins/spade.gif, K/images/graemlins/diamond.gif, 7/images/graemlins/diamond.gif <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">MP bets</font>, Hero calls.

Figured a raise here would allow an underpair to get out too easy plus I don't have much equity against his range anyway.

Turn: (6.25 BB) 7/images/graemlins/heart.gif <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">MP bets</font>, Hero calls.

Same story.

River: (8.25 BB) J/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">MP bets</font>, Hero folds.

Final Pot: 9.25 BB

On the river, JJ pulls ahead and I can't see any hand I beat betting all 3 streets enough to make this a call.

Anyone play if differently? Am I giving a relative unknown too much credit?

[New001]

I think I'd call against an unknown and throw something heavy if he spiked his J out. You can't really rule out AQ or something weird like AJd or a very overplayed underpair.