Any reads? I'm making an expoltive fold here, even though their 3bet is tiny I'm going to assume it's a fish playing a monster pretty bad. Pot size flop bet and half size turn is confusing not sure what to make of it other than they are clicking buttons.

Near the middle of our range can't really call a river bet on a blank. If you've seem them do this before then that change everything and I'd be calling the turn.

Against an unknown, that's what came in my mind as well, probably AA, KK or even QQ. The bets are weird, but interesting. The possibility of him trying to create a rediculous SPR for a shove on the river is out of the question, as this would be 2/3 of the pot. So... Is he afraid of you having a set or two pair after you called the flop? In this case, he's probably checking the river and there is a slight possibility that he folds to a shove. But I don't think this is profitable in the long run. Of course, checking behind is giving away money. I'm folding the turn. As Harvie said, everything changes if we have any reads.

I'm inclined to agree that given the stakes you should probably lean towards the exploitative fold on the turn, unless you have some solid info suggesting otherwise.