7 players left with blinds at 75/150.

SB: 1315
BB: 3980
UTG: 1492
MP1: 1585
MP2: 865
CO (me): 2695
button: 1568

Folded around, and I try a steal with 8d7c. Big stack calls. As to the validity of the steal attempt, it's doable but not necessary here imo: For it speaks that I haven't played many hands and only turned up very credible ones when I have, so I think I have a good deal of fold equity (button has to play tight, and SB is playing pretty tight). But big stack will play decent hands despite my tight image.

My real question is on post-flop play here.

Flop comes Th8c8h, so great for me. BB checks, and I fire 600 into the pot of 975. He calls. I'd say his range is something like any decent pair (66+ can play this way, incuding of course TT and JJ), flush draw, straight draw maybe (I have my doubts that he'd play 97s or J9s but possible), JT, QT, etc. as well as the rare 8, which is going to be bigger than mine.

Turn Jd, pot is 2,175, I have 1,645, and villain checks.

Shove or check behind?

Considerations:

1) I'm not in terrible shape with 1,645 left if a heart hits the river, and I fold to his shove.

2) There's no way he's laying down AhQh, AhJh, AhKh, KhJh, QhJh if I bet.

3) There's also no way he's laying down QQ+, and he'll presumably also call with 99 or JT, possibly any big T.

So, I suppose there are a few calling hands to which I'm drawing near dead here (TT, JJ, etc.), then a few hands (big heart draws with straighting possibilities) to which I'm ahead but that have lots of outs, and maybe 50% of hands that have few outs and call (big pairs, 99). And there are several 2-outers (66, etc.) that fold to a shove.

I guess under normal circumstances it's a fairly clear shove. On the other hand, he's the big stack, and I'm still (barely) second in chips if I end up folding.