I didn't mean to include 44 lol, but yeah I still think JJ or QQ plays this way often enough for you to call here. If he calls flop with these hands, he probably will just shove over your turn bet a fair amount since he's not folding either way.

I'm not sure why you assume he will frequently raise these on the flop, given that BU will fold most of the time and you don't stack off with much worse.

I think you can at the very least stick JJ in there, which makes folding turn a mistake.