2/4 Abs: A3s blind defense w/ bottom pair

[Somekid]

Villain is loose preflop and could be stealing with a wide range. Postflop he's not great, but I've seen him lay down hands.

Did I take the right line here or should I just give up? I was going to bet any turn card.

Hero has Ah3h in the BB
Folded to Villain (Button) who open raises, SB folds, I call

Flop: 8c 3c 6s
I check, Villain bets, I raise, Villain calls

Turn: Jd
I bet, Villain calls.

River:9d
I check, Villain checks.

Also, against what kind of player is this line useful (if ever)?