tough spot, flopping bottom 2 can be sooooo evil.
i would of bet out the flop, with that Q turn only really helping QJ....Like mentioned JJ QQ 66 44 are very unlikely, the way its played the flush draw is the probable hand, (i think if he had a decent J-x he repops the flop to scare off potential draws)
i bet out just under $500 on the turn, but hating my 2 pair if he repops.....if he flats the turn bet i'm check cry calling river
Fwiw, despite the flop now changing he never does that with Jx if he is in anyway competent, it achieves nothing as we'll just fold all worse and ship better.