If I were to c-bet this hand I would fold to a raise. You block a huge amount of bluffs. This flop is really good for villain só you should probably pot control a decent amount of the time

Just because you aren't calling a raise doesn't necessarily mean you shouldn't cbet. Given how wide ranges can get bvb I think cbetting is fine. It depends mostly what he's doing with his pair plus draws. The more aggro he is going to play them I'd lean towards check back, to avoid bet folding incorrectly, but there should be value in a cb with the sizing you chose.

Is he a good/bad player good/bad reg?
Things that I see about the hand:
Pre. I would raise 2.00 insted of 1.75.
Flop. I would raise more than 1.67, something like 2.80. This board is very good for oop player. He has a lot of AT, T9s, 89s, 87s, 67s, Q9s, JTs, J9s, AXdiamonds, that can extract value from. He also have 6 to 8 sets, few straights, and a couple of 2 pair combos. So he is more likely to have a calling hand than a raising hand, it looks scary but it's not that scary as it looks.
Turn. I would fold here as well, all his value range is still ahead even on this card, and all his semibluff hands got way better than ours on this turn. Just a shift eq card, so have to fold.
For me it's wp and I would try to stract more value pre and flop.

Gl!

Turn is a fold. Bad card for your hand, but you should have plenty of 9x if you 3bet a lot of suited 9x hands.

As for flop strategy, you can probably get away with cbetting entire range with around 40% pot size. The preflop range matters here, but not as much as in spots where ranges are more narrow and deeper SPR. Sets is not a concern here with this SPR and this wide ranges. Does villain call offsuit Tx preflop here? If yes, you might consider playing a mixed strategy of betting and checking, but it is still reasonable to cbet range with the big overpair advantage. If no, I would always cbet this flop.

It is probably better in theory (not in practice) to use a larger bet size and play mixed on this flop and JJ should always be a bet with that strategy. It is probably a good 3bet shove OTF unless we assume villain is never raising Tx or draws (give him the nit badge). If that assumption is true you should always cbet.

Villain range on turn:
TT-66,Q9s,J9s,T9s,T8s,98s,87s,76s,AdQd,Ad9d,Ad8d,Ad7d,Ad5d,Ad4d,Ad3d,Ad2d,KdQd,Kd9d,5d4d

Pot odds before rake: 1.96 : 1 or 33.76%
Equity of JdJs vs villain range on Td8h6d7c board: 21.5%

EV Call = (0.215 * $41.62) - (0.785 * $14.05)
EV Call = ($8.95) - ($11.02)
EV Call = - $2.07

Fwiw, I think the cbet is ok but checking back flop is fine as well. Good protection for your range, and equities will be more defined on turn. Will be hard to extract 3 streets against worse, and pretty much only betting flop for "protection" not much value. Big part of villain's range has significant equity. Better check back flop and decide depending on turn/river runout how to proceed imo. Would try to keep pot manageable and not bloated.

As played you have enough equity to continue flop against villain's x/r because I assume he has enough draws in his x/r range. I'd say his range is very draw heavy but most of those draws have high equity.
Turn is the worst obviously. Only 7d would be worse.
Good turns for you would be J, T, and any non-diamond aside from Aces. Aces are bad for you except the Ad. Board pairing cards are also good for you except for the 8d.

On the flop you can expect to win often at showdown against villain's range, and I'd try to get there as often as I can. Even if it takes checking back a street or two depending on how board runs out.