Betting line and sizing on turn for this hand

This is a WSOP C event with 45 players left out of 160.

Questions about:

1) bet sizing on flop. I think the sizing on a A high board that hits Hero's range is optimal, sizing up a slight bit from 1/3 due to stack sizes and flush draws. Feedback

2) turn bet sizing or check. Due to the board texture and the width of BB's range, I debated sizing of bet here or checking. The merits of betting are that BB likely has some outs here and medium strength hand, so I want to deny equity. The question is whether to bet all in (I have set up a nice just over pot sized bet) or to bet a smaller amount and likely call if BB check/jams. If Hero bets turn and is called; will have to assess whether to call a bet/jam; check behind; or bet based on turn card. If a heart or a card that connects to the 8,4,5 comes in on the turn; I will be in a tougher spot. BB is a capable regular who I will likely have to develop a BC range if he check/jams turn or leads out on certain river cards.

As played, I led out for 15k, Villain tanked than check/jammed. Interestingly enough, I was able to pick up on a live read when he jammed and proceed optimally.

But I wonder whether the optimal play here is to move all in on the turn.

Your thoughts?

PT