Villain plays 36/21 and 3-bets 9.9 overall. He 3-bets a ton vs. my BTN steal: around 20% from SB and 15% from BB. I reckon I have much more of a limping hand than a raising hand, but since a similar situation might occur with me open-raising instead of iso-raising, I'm very interested in post-flop anyway.

I would rate villain as a very good player, who balances his c/f range on these boards with c/c and c/r. Seems to have very proper frequencies for open-raising, c-betting, folding to c-bets, raising vs. c-bet, c/r, donk-betting, and so on. Both in single-raised and 3-bet pots. Also doesn't auto-stab when checked to, etc. Just very balanced overall (and exploitive when appropriate).

On to the flop. Betting when checked to is a no-brainer. On the turn, with SPR a little over 2, I got confused. On the one hand I figured he'd fold most hands that I'm ahead of (such as over pairs with backdoor clubs, unimproved 9 with side cards, 87 with clubs), and stick it in with hands that are better than mine (such as any straight, or top two + a little something extra). I also think he would've c/r KK/QQ with hearts otf already. All this indicates that checking might be best. On the other hand I felt like checking could cause a lot of trouble on the river (besides improving to a boat or a flush), and that my pot equity + fold equity were sufficient to pot/commit, indicating that a bet might be best. Who can enlighten me? Thanks in advance.