There is a weight that has broken free from the back of my 99 QX4's transfer case. It is very heavy and about 3" square (just layers of metal with a rubber mounting). I believe it is some sort of harmonic balance solution. I spoke with the dealer and they could not find the part. They suggested it might be part of the rear case . Does anyone know what this is and if it replaceable or needed?

Can you take a photo of the part and post it here?

It's called a dynamic damper assembly. It is replaceable and it is needed. At certain driving conditions unwanted vibrations occur at the u-joint. This damper keeps those vibrations from becoming problematic and damaging to that part of the drive train. For your '99 QX4, I think it might be Infinity part number 113750W701 but you should double check with a knowledgeable dealer to be sure.