How is this for a range ctrl+c from pokerstove
62-37 in your favor.
He could be raising any of those preflop (arguable point). He's undoubtedly c-betting that flop. Your flop c/c and turn check could easily be seen as a draw/weak pair, both begging for a 2nd barrel.
You're showing further weakness by checking the river. He could be betting for value or bluffing missed flush draws. Seems like an easy call to me.
Considering that this guy is gonna c-bet this flop with ATC, I'd think a c/r would be the best move on the flop. You have a strong but vulnerable hand here.
Also if you don't like that range, trim it down a bit. You'll see that you have the pot odds to call any reasonable range here. By c/c'ing the whole way it's really hard to put him on something narrower.