Villain is VP20/PR13 on 42 hands.

I felt his 3bet calling range just slightly hits this board and I put him on a JJ-66, JTs, 87s and AQs-A4s. Please let me know if my ranging is off?

Not sure whether it was correct to check the flop since I was the preflop aggressor. I checked thinking JJ-66 and Qx would bet a lot of times so my plan was to x/c the flop and lead the turn. However he checks back the flop so I ruled out a lot of Qx in his range. At this point I put him on a flush draw, a hand like A7s-A4s ?

OOT I don't believe the Q should be a scare card for me but please let me know if I am wrong. And on the river it's a brick so I decided to go for a value bet but villain tanks and shoves. Can we find a fold by the way he played ?

I have 2.18:1 odds to call and I ran his range(AA,TT-55,AQs-A4s,K8s-K7s,J9s+,T9s,98s,65s,AQo-A7o,JTo,65o) in equilab and we are 88% equity in this spot.

How else could I have played this hand better overall ?