well your ck/r doesn't look strong, so he will be calling with a wide range. But on the other hand the most likely hand for that raise on the flop is a FD and it gets there on the turn so if you bet he might fold a huge % of his range.

If you ck/r and then ck back turn you are showing weakness vs the flush. I think he could bet Ac this way and shove on any river depending how aggro he is.

on 3.3k hands there has to be more info.

I think you have to bet the turn. You range for x/r flop: FDs, sets, maybe 2pairs, so you have something on every run out turn.

• On a flush turn card, you have lots of flush and you dont want to be checking because not all of your flushes are the nut flush and you dont want him to cb with an AcXx and spike a better flush. If you start checking sets and only betting flushes, you are easy to play against imo. I think I'd bet my entire range OTT and readjust if he raises (probably call a small raise and fold river unimproved)

• On a blank card, you still have sets and 2pairs, so you still want to bet your entire range (sets and 2pairs for value and FD as a semi bluff)