5/10: Controlling how many bets go in on the river

[RunDownHouse]

I think I played this correctly, but I want to make sure. Villian sat down not long ago, but he lrr'd TT UTG while 4handed, and I get the general feeling that he's on the LAG side, liking to put bets in with moderate strength regardless of strength shown by others. Other than that, no real reads.

Party Poker 5/10 Hold'em (6 max, 5 handed) converter

Preflop: Hero is Button with 8[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/heart.gif[/img].
<font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">1 fold</font>, BB calls.

Flop: (4.40 SB) 9[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, BB calls.

Turn: (3.20 BB) 4[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">BB raises</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">BB caps</font>, Hero calls.

River: (11.20 BB) 4[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, Hero...

I have the choice to put 1 bet in for sure, or go 2 and risk going 3. If I'm 3bet, how bad are my chances? If 3bet, do I cap?