Default for me would be to 3 bet call. Can flat if you like i guess but you should def not be 3 bet folding in this spot. If he's tight and he jams your'e not loving it but its still a profitable call. The point of 3 betting is sometimes he folds (not a disaster) and when he calls you win more.
I would assume i have 40bb not 50 tbh. A 1-2-4-8 game is effectively as big as a 5/10 game. You can rarely go wrong getting 50BB in pre with Jacks in a cash game even v a tight player. Do you think he ever shoves 77/88/99/22 here? If hes a solid pro he'll be aware of the effective stack he's playing and that you might be attacking his open.
Just because you think hes playing tight doesnt mean to say he thinks you think hes playing tight. Maybe he opens AJ thinks your attacking the straddled pot and shoves? I dunno theres just a lot of hands in my mind he could shove. If hes in any way decent I dont buy it that hes only shoving QQ+ . (other week i was playing full ring live got it in for 100bb from Big blind with AK v UTG (a renowned nit and tightest player at the table who wasnt tilting) Board runs out JJ447 and i win the pot - moral of the story players ranges are usually bigger than you give them credit for)
If he flats go broke on any flop with no overcards. Be wary of Q's -

are a slightly safer cards in my experience (i assume he shoves ak prob doesnt flat with kj or worse ks)
Given stack sizes you dont have to c bet that big on the flop maybe < 35% of the pot. If villain flats 3 bet he prob has a strong holding so don't expect him to bluff you too often.
Jolly Good. This is more like what was going through my head.
I 3bet to 105. Villain flat called. I'd now narrow his range to QQ/JJ/TT/99 maybe? I think he'd also flat with KK and AA a decent amount too. Perhaps AQ? I think your paragraph about peoples ranges being larger than we give them credit for is really helpful Keith.
So pot is £223 We have £300 behind.
Flop
My thoughts here was that I had to bet call it off but not really loving it.
What about a T9x flop? Could we check/fold this?