I'm on the button with QJ. 4 limpers, I raise, both blinds and all limpers call.

7 players, 7bb, flop is 5J6

checks to the HJ who bets, CO calls, I raise, BB, HJ and CO call.

4 players, 11bb, turn is 7

HJ bets, CO raises.

This is always a difficult spot for me - if CO just calls I probably raise TBH but FACING a raise I always believe my one pair is no good, especially when I can't be sure it's "only" going to cost me 3 big bets to show down.

I'm drawing dead to a set or a straight but most likely have 5 outs to beat two pair (actually, depending on the two pair I have more than that, as if the two pair is 57, a 6 gives me a better two pair). The pot's laying me 7 to 1 on a call. That just doesn't feel like enough to continue, even given the strong probability of collecting additional bets on the river.

Will appreciate feedback if there's anything I should be thinking about that I'm missing.

Thoughts?

I just now noticed that if someone has J5, J6 or J7 I actually only have THREE outs.

I don't think you need to worry too much about these three hands, but I still think this is an easy fold unless you have reads that someone here is a loose cannon.
It's also very unlikely you will be able to get to showdown for 3 bets.

just fold, sorry the river was a Q

Sometimes, top pair gets turned into napkins. This is one of those times.