[Lanzalot]

I'm sure that in scenario (B) I would make a curiosity call. I would want to know if he could go for a c/r with AA or KK on the river after having it checked through on the turn. I would also want to know if he could read me well enough to suspect I would bet that K. I would also want to know if he could c/r bluff with QQ or JJ. These are things I would like to know, combined with the actual chance that I have the best hand, and they would make me call if c/r'd. I know a player can go broke making river curiosity calls but here I think you would have to make one.

Scenario (A): you haven't described him as a person that will be betting JJ/QQ here, so just call even though Aces or a set of Ks are somewhat statistically unlikely. It is possible that your check behind on the turn convinced him you only have a pair of tens here at the river so a call is worth it.

FWIW, I think I dump when he c/r me on the flop.