UTG+1 Is a bad aggro player
MP1 seems nitty/straightforward

fold, UTG+1 raises, fold, MP1 re-raises, folds to me in the SB with JJ

Should I call or 4bet?

I ended up calling, BB folds, UTG+1 calls

flop J74r

Should I lead out or go for a check raise?

What's the 3 betting range of MP?. Knowing if it includes unpaired cards and/or 88-TT gives you the answer.

This should be a cap under normal circumstances.

No cap pre and lead out to trap the Guy between you and the pf aggressor (as played) .

No and yes: Cap pre, and DO lead out. On the flop, the UTG + 1 aggro may not be able to help himself and may raise when you lead out, and hopefully your nit (who put in the last raise pre, as played) has a big hand here (e.g., AA, KK, QQ). If this is the case, you will make A TON of bets on this hand.

Also, think through the alternative: If you start raising later in the hand, you're going to tip the strength of your hand, IMO, and not get nearly as much action against these players as if you lead.