ContBet in 3bet pot

First, what is the purpose of your 3 bet pre?
Second, You have to cbet this flop 100% of the time.

Cbet 100%, the board is made for your hand, dry board with no draws and rainbow. I would definitely barrel twice and potentially check back river depending on opponent. This is a very passive line to take considering you hit top pair after 3-betting. Pocket pairs may call considering theres only one over and they may feel you would continue with AK, AJ, TT-AA here so they may feel they can afford one street v your range.

I don't play full ring but that seems like a clear cbet, a ton of worse hands will be calling on that dry board and it's the board of board you'll cbet when you don't have it. He's calling all pairs 66-JJ, and probably KQ/QJ if you think he's taking these to the flop.

Cbet, no advantage to checking back in position that is worth considering. Also if you check back top pair hands on this board your cbetting range becomes very weak. If you slowplay a lot and only worry about value you will just end up value owning yourself and when you play aggressively you will never have it.

I don't like your 3bet. It's purely as bluff with blockers vs a 10% range, but I think it's strong enough to coldcall. Better 3bet hands like KQo, AJo here. On this board, no need to balance your checking range or so. It's definitly not bad to check, but I slightly prefer betting for value. It's probably a 2 street value hand, I think both lines are fine.

Leaving out the 3bet. Against most calling ranges in a 3bet pot with this board how many combinations of hands beat us how is this not three streets or with position bet bet decide on river?

About coldcall on preflop I think its much more better as for me now.
And about bareling on the Flop and Turn.
So thank you all for your answers!)