With only a few bluffs and many, many value combinations in villains range, check-folding is usually the best choice.
Given that there aren't any trips or flushes available, nor many draws prior to the river, the opponents range is heavily weighted towards value hands. AJ, slowplayed sets like 22, TT, or a semi-float with 66 that came good at the turn are possible. That's very dependant on gameflow, and our image. If we bet here and get raised we are almost certainly beat assuming our actions haven't been too aggressive or bluff heavy.
K⋄Q⋄ and K⋄J⋄ are possible but unlikely. K⋄Q⋄ wants to showdown and we lose to the K⋄J⋄ straight anyway. Q⋄J⋄ and Tx want to showdown more than they want to bluff.
If we do happen to have 2-Pair or better at this point, if your opponent is capable turning weak made hands into bluffs (e.g. He has pairs) or gutshots/turned flush draws that missed, sometimes check-raising is a good option to create even greater +EV situations in the future, and deter your opponent from bluffing at too many rivers.