Right, but my style of play is calling the flop raise with the KK and reading him on the turn, since obviously he didn't really test the waters here.

You give yourself the same chance to read how he reacts (just at the turn instead of the river), put less money into the pot, and get to see the turn which could possibly help you out (an A makes it less likely they have an A, a K lets you know you have the hand, a Q or J gives you a straight draw, a heart gives you the nut flush draw if you have the K of hearts, etc.).

If I thought he had something like JJ, I'd raise the flop harder. But I really just prefer calling or folding in this spot typically.

When playing straight forward poker, you raise when you think you have the best hand, you fold when you think you have the worst hand, and you call (if the bet / raise is small enough to give you pot odds) when you aren't sure.