4.40 8 max turn decision

with his stack size I think you are committed here so maybe check the turn to induce a bluff.
nice hand well played

This is an example of don't knowing why are you betting for. You apparently don't want him to fold.

But look to the flop: 6♥ T♦ K♠

I just see a straight draw in this spot. So you bet here to extract value of a worse hand. Sometimes AT, maybe QJ, an unlikely JJ. I put villan in something like:

88-TT, AT-AQ, QJs, JTs, KJs.

When we bet here is to extract value from AT-AQ, 88, 99, maybe JJ, QJs, KJs, JTs.

The turn comes: 9♦
So now i don't like your big bet. Because betting you make him folding almost all the worse hands and calling just with when you're beaten and look he was committed so he had a hand or he is a fish and will commit a mistake.

So i think in this turn he always folds: 88, JT, AT, AJ, AQ, JJ
Call with: 99, TT, QJ <~ here you're beaten
May call with: K♦J♦

When you bet you take away the chance that the opponent semi-bluff his flush draws (ATd, AJd, AQd). Or make a mistake thinking that his pocket JJ's, KJ, JT are the best hand.

I think the better move here is to check/call or bet small according to the villan's style. Villan can bluff this turn shoving or maybe he can think he had the best hand and that you are weak because of their small bet.
Double barrel makes him think that you at least have a K. Checking makes him think you have a T, air or a flush draw.

I will bet small against opponent's who likes make hero calls. They always think a small bet is weak at all and forget to think in hand ranges.

i mean a few combinations give his pairs now a gutshot which is he would not fold.. also fds are not folding
so don't hate betting... you could also bet smaller like 2,2k to induce something stupid from him!

on the other side i also like checking to give him the chance to bluff us off!
but you don't have those kind of information normally!and 18/7 doesn't look that bluffy to me!