Bet the flop. Never fail to bet the flop when you are the preflop aggressor and then flop a backdoor flush draw, with the ace acting as blocker.
In this sequence you made a 3-bet smaller than the standard recommended size (4x). It is also important to continue to act out the initial aggression. So your goal should be to obtein fold
equity from all the speculative hands that called from the BB. And you will get that by betting a big size. It won't help you much to bet 1/3 or check the flop, when you previously under-bet preflop, simply because the value strength of your range won't be very credible.
On the turn you've tried to recover some value, but this could be "read" to mean that you now most likely have the ace of diamond in your range. Because you didn't protect yourself enough from speculative draws on previous street.
The river is definitely not good for your wide range. When I say it's wide, I'm only emphasizing the fact that you bet a smaller size early and then checked on a flop, where you're basically letting a lot of speculative hands improve.
I'm pretty sure you wouldn't play the way you did if you had a hand like AA or QQ.
Greetings.