Would def check raise on the turn:
1) The board is better for hero's range then for villains range
2) You have the nut flush draw and you block AA
4) You could already be ahead
5) You probably have 14 outs (9x hearts, 3x A and 2x 9)
Problem might be that the SPR is awkward as there is not much room to not go all in on turn if you check raise.

The flop is good for BB's range: Equilab shows about 53-47 equity advantage for pre-flop raiser, which is as close as it reasonably gets. The c-bet is very small, so it's possible to check-raise the flop here.

As played, I think turn call is fine. You can put some hands with Ah in the check-raise turn and jam river range. But I would prefer to choose hands which don't have showdown value. This hand does have some SDV.

On river, when he jams, I think folding is fine. You need to only defend half of your range against a pot-sized bet on the river.

If your range for getting to the river is something like:
99-77,ATs-A8s,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,76s,Ah7h,Ah6h,Ah5h,6h5h,Ah4h,5h4h,Ah3h,Ah2h,A9o-A8o,KJo+,QJo,AhJd,AhJs,AhJc,AdTh,AdTs,AdTc,AhTd,AhTs,AhTc,AsTd,AsTh,AcTd,AcTh

(137 combos)

you can call down with

9d9s, 9d9c, 9s9c, 8s8c, QJs, 76s, AdTd, AsTs, AcTc, KdTd, KsTs, KcTc, QdTd, QsTs, QcTc, JdTd, JsTs, JcTc, Td9d, Ts9s, Tc9c, Js8s, Jc8c, Ts8s, Tc8c, 9s8s, 9c8c, Ah7h, 8s7s, 8c7c, Ah6h, 8s6s, 8c6c, Ah5h, 6h5h, Ah4h, 5h4h, Ah3h, Ah2h, QJo, AdTs, AdTc, AhTd, AhTs, AhTc, AsTd, AcTd, Ad8s, Ad8c, Ah8s, Ah8c, As8c, Ac8s

(70 combos)

which is top pair or better. You have a lot of straights, flushes, boats and trips here. So you don't need to call down with second pair.

However, it's close and since you have a blocker to the nut flush, this hand is a reasonable one to call with.