So let's just discuss the hand as played, because I know I raised light, even on the button but I am curious more about post flop play.

Hero BTN $120
Villain MP ~$400
V2 ~$300

No reads on villain 1. Not a reg that I know of. Does not say a word.
Villain 2 ultra passive but somehow is up this session.

Hero has Jh3h villain limps CO limps hero makes it $16. Villain calls CO calls.

Flop 2c4d5c

Villain and MP check

Hero $35

V1 tanks and calls. CO folds

10d on the turn

V1 tank checks.

Hero? Is shoving ever an option here?

Goes without saying, but top up and don't raise light without a full stack.

AP, safe board to c-bet.

AP to turn, shove prob good with V having a lot of draws and small overpairs in range and you having equity to fall back on if called.

Shoving is an option. Villian could be drawing, villain could be on a flush draw, villain could be on the same draw or a higher straight draw, villain could have a mid pocket pair, etc. There's maybe some fold equity there and hitting just your jack may be good.

Without a read, I would consider putting him on a population range and figure out what the general population would have in these spots as well as their likelihood to fold. I think there's a lot of draws the general population has and folds here. I'd also consider my own image so far for the session. If I've been a little card dead and playing tighter (see: getting fewer hands to play) than usual, I think that helps increase the fold equity in these spots.

Without a read, I also consider my image and if it deserves some additional consideration from the table.

Playing junk hands is no bueno at 1/2 99% of the time. Ap i like a shove.

People seem to over estimate fold equity. Villain probably calls with all flush draws, top pair etc. You have position, I'd use it to check and play the river.

I don't have a problem with your preflop raise if you have a full stack. You can't play this kind of poker with 60 big blinds.

Pot is ~50 on the flop and ~120 on the turn. Your shove would be ~70. I'm not sure whether that's enough to make him fold, but unless you're banking on eight outs (two of which may be no good), I guess you follow through and stuff it.

Just let this be a lesson that playing this type of poker is much more sensible with 125+ big blinds.

EDIT: I forgot about the possibility that a jack may be an out, considering the possibility that he has 66-99. That makes me lean more toward shoving.