tricky one, this sort of situation foxes me often too. The fact that he has check-called on flop and turn suggest a drawing hand. He's already put in over half his stack, so it makes sense to me that he had a draw, missed and now is making one last attempt to win the pot the only way he can, with a bluff. I think i would call here, expecting to see something like A-9h .

You are right about the pot odds, but only if you think he is bluffing. It may also be worth it to see his hand and find out some valuable information about the way he plays certain hands. e.g. did he flop a set or two pair and didn't protect his hand against a draw? did he have a flush draw and was willing to chase it down to the end, then make a bluff on the end? It could pay to know these things for later.