Hand Mistake ?

1/2 live cash game Both Player stacked at about 170.

Hero Ac Ad

Villian makes it 15 to go Hero Raise to 40 gets called.

Flop Ah 6h 7h

Villain bets 40 Hero calls.

Turn 10c villian goes all in for 90 Hero Calls

River 3h

When Villian Bets 40 on flop what do you put him on ? A K or Q of hearts ? 66, 77 ? Think Ace is unlikely since 3 are out already.
When villian Jams Turn you have him on a made Flush ? or set of 6 or set of 7 ?

Thinking if you jam flop you have 10 outs vs made flush but if he shuts down you make a big 40 bucks with a set of AAA and also lose chance
of quad AAAA for high hand of hour.
Anyone want yo guess his hold cards ?