Given that he bet-folded the turn, he might not have had much of a hand, and you might have extracted the maximum already. If I had to guess, I could see him have a hand like A high, which put out a standard C-bet and decided to fire again, because he picked up a gutshot. But with just a gutshot and an over, he is not going to continue against even a small raise.
But he is probably also not going to fire again on the river, so if you check-call again, you are just giving him a free card to hit his 4-outer and put you in a miserable spot on the river. With that being said I think, there are different ways to play the hand, so lets break it down.
Preflop
Standard defend against a min-raise.
Flop
With middle set you obviously want to get stacks inside, unless the board runs out in a horrible way like 3-2 or h-h putting out some kind of 1-liner. Any line other than folding is obviously +EV, but if I was to pick one, I actually kind of like a donk bet. With effective stacks of 35BB, 3 bets are enough to get stacks in, and the simplest way to make sure, 3 bets go in, is to just grab the initiative right away and go bet, bet, jam.
This generally look weaker than a check-raise, and some people play very poorly against donk bets. They see them almost like a personal insult, and they might even raise you, in which case you can simply get it all in on the flop. Sure you might miss out on value from some bluffs now and then, but you make sure, a bet goes in, and really you just need to hope, someone has a piece of this board.
Turn
As played 300HPGOD already made a good case for check-jamming to make it look more bluffy. This also price out any draw, which is valuable in an MTT for ICM reasons. If he has a hand like 8h6h, you are happy, if he calls it off, but you are also totally happy, if he fold and give up his chance of hitting one of his 10 outs on the river.
__________________
|