$215 TT vs UTG open

Lead out turn to extract value from all the heart draws + try folding out JJ if possible and even QQ (you have in your range Kx hands such as KJs-KQs, AK etc). Checking behind is good option if you have solid reads that he will turn his weaker pps into bluff on the river and also bet missed flushes plus random Ax (AJ AQo with A or Q of hearts).
Otherwise betting and checking will be super exploitable as on this flop there is rarely any hand that villain folds to 1 barrel.

I agree that turn should be a barrel, however, his flop check back on that board vs 2 opponents looked so weak that I decided to check turn to let him try to bluff me on the river with smaller pocket pairs + missed draws. Also if we would have checked river, I would have bet for value.

For that particular play you need super specific reads.
What is his won at showdown? What is his bet river after opp checks turn %? Aggression frequency on river? His initial UTG opening range? His fold to C bet OOP flop?
These are just few stats that can give us great insight into what he might be doing on the river - or at least make our decision easier to bluff catch or not!

GL

i like your line, but would prob bet like 2/3 of pot on the flop (let us be face up, but it would be easier to play), because then opponents will prob fold all worse hand than ours and jam better ones, but your bet is very good, i like turn check, but river depends on timing and agg factor for river, how much he shows down hands etc. Hard to say