First of all, I think betting the turn is better than a check. If he has nothing to pay you off with, that's fine, it wouldn't matter either way; but your hand is vulnerable with this board and the fact that the opponent could have basically any two random cards.
I fold the river. It should be pretty clear that villain's range here is very polarized--either he has nothing or he has a full house or better. It's easy to be a little blinded to the relative strength of your hand (hey, a straight is good!), but would you be so ready to make a call if you only had a 2? What if you had just A6? Because those types of hands have the exact same chances of winning against such a polarized range.
The main reason for folding is that he is making this wild bet out of position on that particular river card. From villain's point of view, you are holding two completely random cards--I mean, you haven't given him any information to go on during the hand (well, you probably don't have pocket aces or something like that)--the river makes it possible for some random hands to have hit a straight. Even though he may be a fish, is he betting 25X the pot on a bluff knowing that it's perfectly possible for you to have hit a straight? If you had checked to him on this river, it would be a little bit of a different story.
Another factor that could be overlooked is that if you're thinking "Hey, this guy isn't very good at poker, he could be making a stupid play", consider this: even if that is the case, if you fold, his money stays at the table and he'll continue playing stupidly. Some of that "dead money" will presumably funnel to you, so you could consider this a little extra equity that you have for just being at the table--you don't need it all in one hand when the risk is that you're wrong and lose a whole stack.
By the way, what I think that people are thinking here in villain's position is that they don't care about a stupid little pot, they're willing to gamble on the fact that the river hit you and that their bet looks suspicious enough so that you make a "heroic" call and they win a real nice pot. It's actually not so bad of a strategy for someone with the right image. They can bet 2BB's and have you call 20% of the time (I'm making up numbers here) for an expectation of 0.4BB's from the small bet; or, they try the big overbet wherein they only need to be a called a very small percentage of the time to be more profitable. If they're beat, then they're planning on losing their whole stack either way. I don't know if the fish literally think it out this way, but for a regular player who's playing other regular players this strategy is counterproductive from a meta-game consideration.