I would have called this for one reason:

You showed strenght troughout the hand, except on the river were your check indicated that you was afraid someone hit his flush. It was easy for him to put you on a high pocket pair.

Now let's suppose that this guy really had a flush, why would he bet that much?? You would probably have called a 5$ or 10$ bet but not an all-in. So he had the flush, going all-in was not the best move. For this reason, I would have called, putting him on a bluff. Sure, sometimes you'll lose this way, but most of the time (in my experience), the guy is just bluffing.

Here's an example at a .25/0.5 NL table.

I have AK, and raise 4BB preflop. Just one caller and I have position on him.

The flops come K 8 2 with 2 clubs. This guy makes a 2$ bet and I raise him to 8$. He calls.

The turn: 9 of club. He goes all-in for 50$ while there is 20$ in the pot.

That sounds like a bluff to me. I call without any hesitation. The guy shows 2 4 with only 1 club and I win a huge pot.

Edit: I also think your check on the river was the right move. A bet on the river on this situation would almost never win you money. If you bet and the guy has a flush, you will lose your bet. If you bet and the guy didn't hit his flush, he'll fold and won't make a penny out of this bet. In this situation checking I believe was the right move. After, you have to analyse his bet and see if it is worth calling. I would probably have folded to a 10$ bet, but called an all-in. That's poker