QQ, against LP player and JJx flop

[JAP]

Villain is a very loose passive player.
Would most players bet flop, bet (or check) turn, check river?
I decided not to bet because i was scared of J, but after two checks i decided that my hand was the best and a valuebet was ok. Do you fold/call/raise his river reraise?
I would like comments on all streets please.

** 4Runner [Hold 'em] (1.00|2.00 No Limit - Cash Game) Real Money

- Button sitting in seat 1 with $280.30 [Dealer]
- SB sitting in seat 2 with $65.90
- BB sitting in seat 3 with $204.65
- Villain sitting in seat 4 with $214.35
- Hero sitting in seat 5 with $220.30

SB posted the small blind - $1.00
BB posted the big blind - $2.00
** Dealing card to Hero: Queen of Hearts, Queen of Spades
Villain called - $2.00
Hero raised - $10.00
Button folded
SB folded
BB folded
Villain called - $10.00

** Dealing the flop: Jd, Jc, 5d
Villain checked
Hero checked

** Dealing the turn: 4s
Villain checked
Hero checked

** Dealing the river: 3s
Villain checked
Hero bet - $20.00
Villain raised - $40.00