Villan is typical shortstack donk.

PokerStars No-Limit Hold'em, $1.00 BB (6 handed) from (Format: Bet The Pot)

saw flop|saw showdown

MP ($112.70)
CO ($55.95)
Button ($77.35)
SB ($43.35)
BB ($107.05)
Hero ($135.85)

Preflop: Hero is UTG with , .
Hero raises to $4, 3 folds, SB calls $3.50, 1 fold.

Flop: ($9) , , (2 players)
SB checks, Hero bets $7, SB calls $7.

Turn: ($23) (2 players)
SB checks, Hero bets $20, SB raises to $32.35, Hero calls $12.35.

River: ($87.70) (2 players)

Final Pot: $87.70

I don't see any problems with winning or losing a half buy in here. I really don't see problems with the continuing of betting and calling $12. If you get beat by a better kicker or a set you have to take your lumps.

against a shortstack, i think you played it fine. against a bigger stack, you could consider checking behind on the turn depending on a read as your kicker is weak and the flop is pretty blank. often you have him in really bad shape and can check and let him bluff you and/or keep the post smaller if he has you beat, because you will either get check raised on the turn or make a hopeless hand fold. It all depends if you think he's an idiot with a lesser ace.