I don't know whether it's correct play, but it think i would (nit-) fold in both situations.
looking at the JJ hand we have to be right 2.61/6.25 = 42% of the time, which im just not conviced we are seeing as he has now fired 3 bullets. Plus, in my experience a bet sizing like that screams that he want's you to call.
My problem with the TT Hand is that if we are calling the turn i think we have to call action on the river most of the time, and by the river the pot will be 2.43+2*0.93= 4.29$ (minus rake), which is more than enough to put you all in if he wants to. plus any J,K or A on the river will make a river call even more uncomfortable. Now theoretically, he could know that the Q on the turn is a good card to double-barrel bluff but im not sure he does that enough for the call to be worth it.
I could be very wrong, but that's my take on it