7 handed game blinds 100/100/200 PLO

HERO stack $75000
VILLIAN stack $40000

HERO is in BB with KsJs9s5h
Action folded to HERO
HERO Completes 200
VILLIAN is in straddle RAISES to 700
HERO calls

Pot $1500 FLOP is 9 4 3 rainbow
HERO checks
VILLIAN bets $1200
HERO raises to $3200
VILLIAN re-raises to $9000
HERO ???

This is a live PLO hand I played recently with which I had some trouble with so I thought I would share it with the great minds here on runitonce to receive some advice/analysis on what is the best way to play this hand vs villain.

Villian is a tough regular, very aggressive and tricky. The type who will put pressure as soon as he senses any weakness and will always follow through. Preflop I think it is pretty standard limp call with my hand. Flop is where it got tricky. I think I could've gone either way check-call or check-raise. Decided to check-raise blocking 9 but this play may have been a mistake vs this particular opponent. Would like to hear what you guys think. His re-raise was the interesting part. During the hand I'm thinking he would not have done that with a strong made hand, I think he would rather call and let me barrel if he had had set. I think he has a lot of wraps, some 9-4, 9-3 two pairs or maybe even just one 9. What do you guys think his re-raising range is there and how should we proceed with the hand as played?