SH 66 UTG v CO -any point in betting postflop?

I think you can bet flop once to try and just pick it up then just give up turn. Especially on this card you don't really pick up any fold equity. Can't see hands like T9s for example folding here.

You can stab once but imo it is one and done. Give up OTT.
I also want to point out that you have too small sample size. Also villains flop fold to cbet is not that low. Bet sizes often being between 1/2pot and pot, that fold2cbet is about optimal.

I think it's fine not cbet this board.

Board hits his range of mid pairs, sc and suited broadways and it doesn't hit very well an UTG range.

He has only 12 combos of better hands that you actually make him fold (77-88) and since he probably don't fold much you are easily floated OTT or you spill chips OTT and OTR. I rather cbet some backdoors like AT of clubd cause it's easier to barrel and it can actually hit some decent midtoppairs and fds or sd.

As played i like your turn barrel if you plan to barrel non hearts river.

If he calls to cBets a lot why bet with a weak hand if we are not going to bluff turn aswell?

what reads do we have on our opponent when he is checked to? will we get checked back on flop and maybe turn if he does not hit?

If he is not folding much we can skip the cbet...

I agree with Avskum and nitrol.

CO does not fold much, when we cbet flop or turn. Our hand is not really strong enough to play a big pot with. There are two overlords on the flop and at least the J hits his range pretty well. In this spot I would think about betting twice. If I do cbet, I play one and done. If he checks back on the turn, I could think about another bet on the river, depending on the reads and on the river card.

Against a passive player I easily check with low value hands and bet with high value hands. A very easy system We can x flop here.