Be mindful that you're posting on the beginners forum so you'll get beginners replies (including mine). Just writing it up slightly more readable

Stacks $50. Blinds $0.25/$0.50

Hero:
folds, Villains calls $0.50, folds, Hero raises to $2, folds, Villain calls

Flop:
Pot $4.75
Villain checks, Hero bets $4, Villain calls

Turn:
Pot $12.75
Villain checks, Hero bets $8, Villain raises to $18

Ok, here are my thoughts - try to read your own hand. What does your opponent think you have? To me, you look a lot like JsTs.

Remember that if he calls your $8 bet on the turn the pot will be $28.75 and you'll both have $36 behind. That's a bit of an overbet, and if you wanted to get all-in with your hand you might have wanted to bet bigger on the turn - especially if you are concerned about someone else on the draw. Your turn bet is just small enough to make him think that you may be on a draw yourself. With the rainbow completing any backdoor flush draw you may also have had on the flop are now no longer possible.

Alternately you could have ATs, T9, T8 and similar.

When the villain plays what you call uncharacteristically passive - it feels a lot like a slowplay with a monster. A monster in this case could be a made straight - but it could also be a lower set.

The raise is small - he definitely wants you to call. And if you do call the pot will be $48.75 with $26 behind - a call of a bet is almost automatically an all-in.

If you are 100% certain that he's holding a straight at this point the correct play is to call and fold the river if you do not make a full house. My problem with that approach is just that you can't be 100% certain. Regardless how good and aggressive he is I simply cannot rule out a lower set for him here. ESPECIALLY because he explodes into action on a turn card that doesn't help any straight draws when your betting goes a bit weak.

As to the other part of the question - should we raise? I don't think we should.
Let's say he has a straight draw that gives him 8 outs, so he improves on the river about 16% of the time.
Let's say if you re-raise the turn he folds 100% of the time.
If on any missed river he folds if you bet and checks if you check you would be right to raise the turn.
However, I think he will bluff his missed draws on the river often enough that it will be more profitable to let him do so.

This gives rise to the question if there are any river cards we would fold to if we check and he shoves - particularly any Q, J, 7 or 6. Again, I don't think so - he would also shove with missed draws sometimes as well as two pair and set hands that we all beat.

Personally, I think his most likely hand is 88/99 and the best way to extract value is to call the turn and check/call the river shove.

There are no hands in his range that you beat that will call any further bets or raises from you.