I have never played these stakes, and I know these games tend to be really nitty so I might be either out of touch, or delusional, but StueysKid's analysis seems way overly pessimistic to me.
The operative stat in this case is going to be MP1's fold to 3-bet, but we're without a read so we don't exactly know. The other factor, is that the multi way nature of this pot means that I think contrary to prior analysis, MP1 is peeling your 3-bet with a wider range than normal....
Think about it. At 10NL, it's highly unlikely that the CO and the Button are flatting premium hands to back raise a squeeze from the blinds. I mean, unless you have been very conspicuously 3-balling every single LP open, you're not getting trapped at 10NL. People aren't often squeezing light from the blinds at these stakes, so MP1 isn't operating on the logic that "Oh well, the CO and BTN called and then the BB squeezed, they might be flatting really strong hands they're going to jam with after I call so I'd better tighten up my range to this squeeze play." This is really overthinking the state of 10NL. MP1 is more likely thinking "okay, I raised, got two callers, and then then the BB raised. The CO and the BTN might come along and if I hit I can win a huge pot." His range is probably pretty speculative.
While I think that pre flop, flatting in this case has merit, raising for is fine because I think you're going to get it. I think that MP1 and others are mistakenly going to try to flop sets or something with suited connectors often enough that there is value in your squeeze. I mean, are the games really that nitty where we're saying that it's too thin raise for value against an MP1 open and two calls with JJ?
So you 3-bet and get called in two places. I think this is a spot at 10NL where we can actually be nearly certain that you do have the best hand. I think at the lower stakes you get jammed on pre by AK+. People at this stakes are mostly terrified of post flop play, so I think that you can pretty much eliminate at least AK, QQ, and KK from everyone's range. People are afraid of bricking AK, and worried about overcards with KK and QQ. Even AA tends to get a little too jumpy and 4-bets your pretty often, so I think JJ is good here a tremendous amount of the time.
Flop come down 665 two club. There are no overcards, there is a flush draw, and we have a very shallow STP ratio. If you got outflopped by 55, 56s, 67s, 68s, then that sucks. I see basically no circumstance in which I'm willing to bet/fold here. I also think checking here is terrible for reasons that are pretty obvious. So let's talk about betsizing. I don't think the betsize is that awful. At this level, I don't think your opponents are reading too much into your sizing, they're going to be very consumed with the strength of their hand. And as far as balance is concerned, don't worry about it yet. Maybe they'll think something like "well, he raised pre flop and then made a big bet that looks like it doesn't want to be called, I have 77, 88, 99, TT, he probably has AK, I'm going with it."
So you c-bet 3.75 and get called which does not bode well for us at all. I'd expect flush draws and overpairs to jam the flop, so when MP1 just calls with a player behind, I think you're drawing to two outs here a lot, although I could see him flatting the nut flush draw with a speculative suited ace. When the turn comes same 4 and you don't have a club, it's pretty much finished for you. At 10NL, you MIGHT be able to find a fold on the turn, and I'm not kidding, but I can't really blame you calling it off getting better than 3.5:1.
My guess is that you lost to some hand with a 6 in it, but given the potsize on the flop and your flop bet, I don't really think there's anything that you can do. As StueysKid mentioned, bet smaller on the flop but I mean, pot is bloated so what can you do?
I def. think 3-balling JJ pre is fine here though. I mean if you can't 3-bet JJ here, what can you 3-bet? Bluffs, and AK+?