Stars $10 - jj overpair 3 way

[JSampras1]

I'm new to 6 max, so i'm trying to figure out if i played this wrong. I think i should have raised more preflop, but besides that, did i play this wrong?

Limp caller was passive and bad, so i wasn't really worried. Villain who raised is 67%/51%/AF 4 so I am ahead of most of his hands. He didn't reraise the flop, and 445 is pretty good because there's only 1 set and quads possible. It's 3 way and my hand is vulnerable, so i think i have to push here right?

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Button ($4.75)
SB ($1.40)
BB ($9.65)
UTG ($17.20)
MP ($14.75)
Hero ($9.70)

Preflop: Hero is CO with J[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/spade.gif[/img].
<font color="#CC3333">UTG raises to $0.3</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $1</font>, Button calls $1, <font color="#666666">2 folds</font>, UTG calls $0.70.

Flop: ($3.15) 4[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">UTG bets $0.2</font>, <font color="#CC3333">Hero raises to $2.25</font>, Button calls $2.25, UTG calls $2.05.

Turn: ($9.90) 6[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
UTG checks, <font color="#CC3333">Hero bets $6.45 (All-In)</font>