Stacks:
Hero 1800.
MP 2200.
Button covers.

Preflop:
Table folds to MP. MP raises to 70. Button calls. SB folds. Hero calls with 7 8 in the bb.

Flop: (220)
9 8 6

Hero checks. MP bets 180. Button calls 180. Hero ??

MP is aggressive. I don't think he has a hand, he's just saying, "Give me your blinds, bitches."
Preflop, I have just a suited connector out of position, but I'm closing the action and getting a discount in a 3-way pot.

If it turns out that the button has hearts, it'll be tough to move him off his hand. I don't really want to play the turn with first action and a whole stack behind, though. Thoughts?

You basically said that you don't think either player will fold their hand.
It's hard to get play money players to fold their hands.
You can just call and fold on the turn if you don't make your draw and/or aren't getting a good price.
Or you can just shove the flop and expect to have 6-14 outs.

Pretend it's 2/5 real money. Does that change your answer?

1. I misread the OP and thought he said MP did have a hand.
2. Since he doesn't, raising is far and away best here, especially if you think the other guy has a heart draw.

I think this is why you don't play suited connectors out of position.

As played, flat call the flop and check-raise on a favorable turn card.

I raised and called a push. The button had A 7 , which is a slight favorite to my hand.