NL10 JJ facing 4bet

[Landogarner4]

Poker Stars - No Limit Hold'em Cash Game - $0.05/$0.10 Blinds - 6 Players - (LegoPoker Hand History Converter)

Hero (SB): $10.10
BB: $5.35
UTG: $6.75
Villain: $9.25
CO: $7.85
BTN: $12.00

Preflop: Hero is dealt J[img]/images/graemlins/club.gif[/img] J[img]/images/graemlins/diamond.gif[/img] (6 Players)
UTG folds, <font color="red">Villain raises to $0.30</font>, CO calls $0.30, BTN folds, <font color="red">Hero raises to $1.40</font>, BB folds, <font color="red">Villain raises to $3.50</font>, CO folds, Hero ???

Flop will be ($7.40), Villain has $5.75 left.

Villain is 32/21/2 over 40 hands. Have never seen him 4bet so I put him on QQ++ and AK?

I have to fold, right? Villain doesn't have enough behind to make trying to flop a set profitable?

Could I have cold called the first raise preflop? CO calls raises very light.

Is this the right way to think about this? I'm just cutting my teeth here.