Fold the 2nd nuts?

9/7 over how many hands?
FT3-bet?

Just taking 9% to the flop: { 88+,ATs+,KTs+,QJs,AJo+,KQo }
If Villain C-bets any pair or draw, that's 58% of his range
If Villain also C-bets any 2 overs, that's 94% of his range

call it 100% C-bet here

OTT, not much changes unless Villain decides to check behind w/ AK instead of 2 barreling. Maybe we can assume Villain checks behind w/ TT,99 w/o a heart, but maybe not.
Any idea of whether Villain will check behind IP OTT w/ mid showdown value hands??

OTR, The hands in Villain's starting range w/ a heart that you beat is 8 combos: 3@TT, 3@99 + 2@88.
The flushes w/ an A are 12 combos: 3@AA, 2@AK, 3@AQ, 3@AJ, 1@ATs.
Maybe he has A9s,A8s... opening range could be wider. Maybe he has 77,66, same logic. I don't think he fires 3 streets w/ 77,66, though.

So ~3/5's (~60% ish) of his flushes beat you, assuming he bets worse than 2NF OTR. Would Villain bet sets here?