Looks like villain is TAG, loose TAG, good LAG, or bad LAG, can't tell much else. What does the phrase "bet big every time I've taken 2 hands off him with a turn raise so far" mean?
You don't necessarily need to call preflop, it will depend on what the other blinds are like. As default I fold but I think most everybody else set mines, but I don't think it's as profitable as people think. Although on certain tables I will call depending on stats, reads, images, positions, stack sizes, and action ahead. When my skill level increases so will the number of hands I call with. Something like QJs is different though here, because you can float flops with that hand, and pick up draws on the turn and stuff. You can't do much with 33 postflop unless you hit a set, or there is a dry board with a Q/K/A that you want to bluff float. If people 3bet behind you then you can't call or 4bet light, and if somebody calls then your float potential on the flop is destroyed so you need a set or OESD when the flop hits to continue.
Raise bigger on the flop for value/protection to 80% pot of $5.25, maybe a little more, and the same amount with bluffs here since he may be a decent player and you want to use unexploitable bet sizing against him. You want to get a good amount of money out of 66/22/an Ace/65s/54s/TT+ so you should raise bigger.
Here's a possible range for villain to continue with on the turn, although some of these hands he may fold preflop, or 3bet the flop with, or fold on the flop:
TT+,66-44,22,A2s+,76s,65s,54s,AJo+
The 2 is an absolute atrocious card for you here. You can't get any better hand to fold with a turn bet unless he has 55/44/54s somehow. You can't get two streets out of 22, plus KK-TT/54s will fold. Check here.
Just fold on the river, he's not betting KK-TT/54s/22 here. Your equity is literally 1% here when he bets. You need 30% equity to call, and 30%+ of his range is not KK-TT/54s/22, those hands make up 1% or less of his range. Good luck, Yojimgari