A5 - A high board - BTN vs. BB - villain check/raises

Bet flop higher, it's very draw heavy.
As played it's interesting as you may be inducing him to c/r with your to small bet, although maybe this stake it is more unlikely. I think a fold is fine.

I don't like betting flop with non vulnerable showdown hands. I'd like to give free card to villain and call a bet on the turn.

Depends on read but I probably call a bit unless T or J or spade comes. Seems bluffy to me cuz you induced him with small bet. Beting small is ok imho, but you need to be prepared for reaction to small bets..

I would prefer checking back. You have a good showdown value but you definitely dont have 3 streets of value. He shouldnt have much value himself. All the monsters on this flop 3bet preflop.

I am not concerned about his possible draws. If something gets there and he starts to be aggressive just let it go. So I would go for a check back flop and then call turn and river depending on the runout and his sizing. Or bet turn and then river small.

If you bet on the flop I would just fold to his raise. If he just called I would go for a check back turn and call river. Classic pot control line of bet/check/call.

its 1/2 cbet on the flop - why would you say villian has been induced? I dont see any induce here.

You may call the flop and re-evaluate the turn but vs 58BB villian it would be hard to play postflop i he continues the aggression.

I would just muck on the flop and move on.