Does anyone shove over here? I think folding may be too gross, but this was a tricky spot because I didn't really plan ahead for a 4-bet ahead of time, mostly because I wasn't expecting one.

Villain is 20/10 over 40 hands, bit on the passive side - his ATS was 13%... I really have no idea what this 'proper' 4-bet size means considering I don't think I've ever seen one at this level, but I'm guessing its like polarized to either the nuts or some garbage hand not willing to take shit from a 3-bet.

PokerStars No-Limit Hold'em, $0.10 BB (4 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Button ($17.30)
SB ($10.25)
Hero (BB) ($10.65)
UTG ($11.90)

Preflop: Hero is BB with Q, Q
1 fold, Button bets $0.40, 1 fold, Hero raises to $1.60, Button raises to $3.50....Hero?

Worst part about this hand is I don't really have any history/reliable stats. What type of range would you guys assign an unknown here who's appears a bit on the tight/passive side?