[how_can_losing?]

He has a flush draw and lots of BD draws that would be very, very well disguised, and doesn't want to get blown off the flop. I think flop check is good.

Turn raise, I don't know. Would you really check behind two pair/set/AK on such a drawy board? Since you are more than 100BB deep, I think you would be unlikely to check behind those hands. If villain is capable of 3betting light he might be capable of recognizing this.

Depending on villain I might just call turn and VB/shove river if I hit, and bluff if the heart draw hits, although lots of times people don't believe BD draws. Still, you are huge implied odds to call the turn with probably 12 outs and maybe 7-9 more bluff outs.

A river bluff will probably cost you the same as the amount that you raised on the turn (or even less). So calling turn seems to give you more options.

I'm not saying turn raise is bad, though. If he calls and you hit, you get his stack. He will also have to fold a lot of one pair hands that he doesn't want to play for stacks, and of course air.