[dave44]

See the thing is that on this flop, a check-raise is really only going to knock out worse hands (Q and J highs) and maybe some stronger aces, although you say he is adjusting to your aggressive play so its tough to tell whether he'll take AQ to showdown here. Since you're seeing the river with your flush draw, you're likely going to take the pot away from those worse hands anyway the times he doesn't bluff the turn and river. So while I agree the flop check-raise is +EV, check-calling the flop and turn UI is probably higher +EV since you'll be stealing the pot so often anyway, but with a smaller investment on your part.

The flop check-raise would be automatic here if you held jack high since then you won't ever be winning unimproved.