$5 NLHE 6-max: Very tough turn decision with combo draw

5NL 6-max zoom on pokerstars. Villain is unknown.

Effective stack sizes: $7.46
Hero (BB) is dealt 9h 7h

SB posts $0.02
Hero (BB) posts $0.05
UTG folds
Villain (MP) raises to $0.10
CO raises to $0.40
BTN folds
SB folds
Hero (BB) calls $0.35
Villain (MP) calls $0.30

$1.17 in pot (3 players)
Flop shows Th 9d 8s

Hero (BB) bets $0.77
Villain (MP) raises to $1.54
CO folds
Hero (BB) calls $0.77

$4.12 in pot (2 players) with $5.52 behind (effectively)
Turn shows 4h

Hero checks
Villain bets $4.12
Hero ???

What is our plan here? Are we getting the right price to call the turn? Should we shove over the top? Should we fold? If we call and miss our draw, what are we going to do on the river?

Hand is butchered.

Fold pre and X/c flop

+1. We aren't closing the action, don't have great implied odds, have positional disadvantage, and have weak card advantage. No reason to play 97s here.

Better to x/c flop and turn, and x/f river unimproved. As played, shove/fold is probably neutral EV. We have decent equity against JJ+, which is probably most of his range, but rake is going to be the shove no longer profitable. I don't expect many people to be 3-betting light like JQs/109s, or 3-betting 1010/99/88 very often especially IP. Thinking he more likely has QQ+ here from bet sizing PF and turn bet sizing. Don't think JJ goes nuts like this.

Lots of spew in this hand but others have already explained why.