Sort Your $*%&in' Life Out!

Settled in back home now so putting in a bit more effort on the poker front. Done some work on my C-betting and although I think some of it's down to run good + sample size my red is just better than break even which is fantastic.

Poker Stars No-Limit Hold'em, $0.02 BB (6 handed) - Poker Stars Converter Tool from http://www.flopturnriver.com

Button ($2.25)
SB ($2.07)
BB ($1.60)
UTG ($1.60)
Hero (MP) ($2)
CO ($3)

Preflop: Hero is MP with Q, Q
1 fold, Hero bets $0.08, 1 fold, Button raises $0.20, 2 folds, Hero calls $0.12

Flop: ($0.43) 2, A, J (2 players)
Hero checks, Button bets $0.20, Hero calls $0.20

Turn: ($0.83) 9 (2 players)
Hero checks, Button bets $0.42, Hero folds

Total pot: $0.83

Results below:

Spoiler: Show

Button didn't show

At the time he was an unknown. I sometimes flat my QQ to 3bets and I sometimes 4bet. This was just one of the times I decided to flat it, usually lean towards 4betting (probably always should at this level especially when im OOP). Is my call then fold line ok? Or is his range so weighted towards Ax and TT+ that I should just fold the flop? I'm aware that'd make me pretty exploitable but I doubt anyone is going to take note of stuff like that at this level and when they do they try to run you over which makes them play awfully usually.

i prefer 4betting to .44 and cbetting the flop if he calls as you can get his TT JJ to fold pre and KK to fold on flop with an A on flop(ideally you get a Q high flop). if he raises your cbet it's a fold, and if he shoves pre i think its a fold as you're pretty much against flipping with his AK and behind his KK and AA.