This is a common spot I'm not feeling happy about. We're OOP with a small on a (low) paired flop against an aggressive villain, without initiative.

Our hand has little chance of improving. Villain will most barrel.
In the hand below I just folded. Of course the other option is calling, but if we're not calling turn barrels on certain cards that's the worse choice. So I guess what I'm looking for is if c/fing is standard, and if not what turn cards you'd generally call a barrel on.

This hand villain plays 34/26/2.5 over 100 hands.

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

MP ($15)
CO ($25.15)
Button ($22.70)
Hero (SB) ($28.95)
BB ($19)
UTG ($22.85)

Preflop: Hero is SB with 3, 3
1 fold, MP (poster) checks, 1 fold, Button bets $1, Hero calls $0.90, 2 folds

Flop: ($2.50) 2, 7, 7 (2 players)
Hero checks, Button bets $2, Hero folds

Also, how would you play a hand like KQo in the same situation?