Hero: probably ~25/20 at the time (table was full of nits, was stealing everyone's blinds). Normally 13/9
Villain: 39/5 over 41 hands

I'm putting him on a set here. What to do? Was I correct to raise the flop? I never know how to deal with donkbets

I like almost everything about how you played this hand, with the exception of the raise size on the flop. There is no need to 5x his donk bet if you aren't planning on committing to the pot. A raise to $0.25 to $0.30 is sufficient to give you the information you need to know and this would have saved you more than 10bb which is 100 hands worth of winrate at $2NL.

Once he ships it, you have to fold, because if you stack off here then he was correct to set mine you pre-flop and you would be the one guilty of overplaying your hand.

At 2nl id ship it. Vs unknown villain, you will see Jx a lot.

put all of your chips in the middle

Someone passive playing 39/5 isn't usually raising post-flop unless they have it.

The donkbet itself doesn't mean nuts, but after you pop him, and he re-pops, I think you're done with the hand unless he has a history of spewing with just a pair of Jacks, which I'm assuming we don't have yet after 41 hands.

41 hands aint really enough to assume he's a strict passive player. Often run into top pair weak kicker hands in these situations at 2nl.