Cbetting turns villains hand in a complete bluff on this board. It's true though that if he cbets he can check back turn and fold to a river bet especially on a A high flop. So he would have lost less to better hands.

Pros of villains line with his specific hand are (I think in order of importance on this A high dry board):
1. a turn card can come that give you a draw or something to which he can valuebet you
2. his line might seem suspect which make you call a turn bet lighter
3. you can't bluff raise him
4. he can snap a turn bluff from you (which on this specific board you might not do much, but maybe a turned draw)

I don't like villains call on the river because of the rivered flush.

If river was a blank I'd just call with some top of my range hands to randomize how often I want to call with my bluffcatcher hands. Only if I expect you to be bluffing there sometimes ofcourse.