I recently purchaced a 00 zx3, very happy so far, put a magnaflow on, a mac intake, and eibach pro kit this past month.
The problem I am having is that my right rear seems to be squeaking over bumps, and hard side to side turning (pylons), minor but it is there, this seems to have started about 4 days after install by a local shop. I did notice that with somone in the back seat this problem is gone.
Mine squeaks all the time. I think mine is due to all the urithane bushings in the rear (I changed out every bushing).
I was going to try some P51 shims (a guy on another board sells them). They take up the air space in the rear shock setup. I don't know if this will cure the problem but I am going to try it when I get around to it. Possibly this winter I will install them and find out next spring. Where yours goes away with weight in the rear I would say the shims may cure your problem.
I have a new wrinkle to the squeking. I ordered the shims this evening, then the wife and I went out. It has been raining here most of the day, and the entire time we were out, funny thing is that the squeak was not to be heard the entire trip ( heard it maybe twice I think). So, is this maybe a differant issue?