BvB with marginal hand NL10

[Jailblazers]

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

MP ($10.90)
CO ($13.80)
Button ($9.55)
Hero ($10.30)
BB ($7.10)
UTG ($5.65)

Preflop: Hero is SB with K[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/spade.gif[/img].
<font color="#666666">4 folds</font>, <font color="#CC3333">Hero raises to $0.4</font>, <font color="#CC3333">BB raises to $0.7</font>, Hero calls $0.30.

Flop: ($1.40) 5[img]/images/graemlins/spade.gif[/img], J[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">BB bets $0.8</font>, Hero calls $0.80.

Turn: ($3) 2[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">BB bets $1.1</font>, Hero ?


I'm not sure how to play these types of hands. Villain is somewhat loose-passive.

Did I play this hand too passively or what? I'm not sure what leading out on the flop would accomplish. How many times is he pushing me off the best hand here?