Live game in Casino, blinds 2.5e/2.5e

Villain is young hooded player, about 25. Sober, silent, observing game.
Seems to be regular, have seen him few times in same place.

He has been steady winner, not showing bad hands in the past, rarely going to showdown. Made one great call with second pair against a bad player. He covers me, showed a set once for a big win.

I've played few hours and not shown anything out of the order. Slowly grown my stack to 515e. I think he views me as a competent player, we haven't played in same hands that would have gone far.

Villain opens CO to 7.5e
Hero calls from BB with T7

I'm thinking he has a wide range and he is good enough player to fold to a raise on flop or turn. Also we are very deep, over 200BB effective stack.

Pot: 17.5e
Flop: 458

Check, Villain bets 15e, Call

Villain would CBet his entire range but his betsize is bit big so I am thinking to not check/raise him here but instead look if the turn card allows me to do something, also I can always hit the gutshot I got.

Pot: 47.5e
Turn: J

Check, Villain bets 35e, Call

Now I'm 100% sure he is value betting a good hand and J gave me very sneaky double gutshot. His bet is large and I quickly fudged that I need to get atleast 80e from him on the river if I hit my hand just to break even and made optimistic call that I can get paid off if river card is good.

Pot: 117.5
River: 9 (BOOM)

What should we do? Lead in or go for check-rase?

My stack left: 457.5e, Villain covers me.

QT would be nuts but I don't think there is any QT in his range, QT would be disgusting but apart from that I think I have the best hand.

Your speculative math is way off haha. To call the turn you actually need to make over 100e on the river, and that's 100e every single time. Which is definitely not going to happen. You don't even have the best hand all the time! You should be a lot more conservative when estimating implied odds for this reason.

Making things worse is that you're out of position and there are few disguised outs -- you're hoping for specifically a non-heart 9 as a 6 puts 4 to a straight and if a heart comes many players will (not unreasonably) assume that you are on a flush draw with your line.

Best line would be folding preflop. As played either c/r or fold flop. Our draw is trash, not because it is a gutshot but because it is very hard to get paid enough if we hit it. Once V bets two streets on this board I'm not going to try to get him off the hand and we have nowhere near the right implied odds to continue.

You shouldn't be in hand by river. Once you get there, bet pot and hope he has something to pay you off. Your call/call line looks strange and he is likely to put you on a slow played 87/set or air and not bet.

Even if he does bet, when you check/raise he is going to put you on a big hand or air and isn't likely to pay you. The check/raise line has a better chance of getting paid something but is less likely to get paid enough to justify calling on turn.

You mention villian is rarely going to showdown meaning he is either folding to aggression or putting it on himself yet you take a passive line calling down. Knowing he will likely atleast cbet once and if you are not comfortable playing OOP then just fold preflop.

If you want to play you either have to 3bet pre or call and plan on c/r most boards. However, you are going to need to know if he is a one and done player and whether he calls down loose.