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@dberry hit on it a bit, but this may help.
Weight is different than mass. Weight is essentially a function of your mass and the density of your body against the density of the medium that you are in.
If your body has a mass of 192lbs, and displaces 3 cubic feet of water, then you will be exactly neutral in salt water, and roughly 5lbs negative in fresh water. The amount of water you displace is 3 cubic feet in either direction, and the mass of your body is always 192lbs, but 3 cubic feet of fresh water weighs 187.2lbs, vs 3 cubic feet of salt water that weighs 192lbs.
Think about it in terms of a scale balance. You have you and your gear on one side and on the other is a vessel with volume equivalent to the amount of water you displace. In the example above, you have a mass of 192lbs, and the vessel is 3 cubic feet. In fresh water, the mass of that vessel is 187.2lbs and with salt the mass is 192lbs.
When you change your exposure protection you are changing the amount of water that you displace and replacing it with a combo of neoprene, nylon, polyester, and air. The volume that the suit displaces is equivalent to the amount of lead you have to add. The "rule" is roughly 2lbs per mm of neoprene in salt water. We can approximate from this that 1mm of neoprene has a volume of roughly 2/64cf. A 8mm suit *for easy math* in that case would displace 16/64cf of salt water and require 16lbs of lead to sink. In salt water it still displaces 16/64cf of water, but to get the amount that it would require in fresh water we have to use the following. 16*62.4/64 which is 15.6lbs to adjust.
The real difference starts to show up when you have to adjust for your total body and rig weight. If I'm diving in salt water with my 6.5mm, the math is crazy. I weight 270lbs, my wetsuit weighs about 10lbs, and my doubles rig weighs roughly 120lbs. Let's assume I'm neutral in fresh water, so my rig and body has a mass of 400lbs. 400lbs means I'm displacing 6.41cf of water. In salt, I still displace 6.41cf, but the mass of that water has changed from 400lbs, to 410.24lbs so I have to add 10-11lbs of lead to my rig to allow the balance to level itself.
The basic algebra requires the following
mass of diver+rig+exposure protection weighted appropriately for either salt or fresh*in air on the surface that is weight on a scale btw*
mass of 1cf of salt water=64lbs *both masses of water will be slightly different based on salinity, mineral content, etc*
mass of 1cf of fresh water=62.4lbs
If weighted for fresh
massdiver*64/62.4
If weighted for salt
massdiver*62.4/64
Most people aren't going to put themselves on a scale in all of their gear to make the adjustment, and if you infrequently dive one or the other, adding 6-10lbs for salt, and removing 4-6lbs for fresh is usually sufficient. In either circumstance you'll be slightly overweighted by 2-4lbs, but it is often impractical to do a full weight check, especially for the salty stuff if you dive it infrequently.
Note that 64/62.4 is 1.026, and 410.24/400 is also 1.026, hence the 3% rule.
none of this is meant to replace true weight checks, but that's the science behind it. I'm very tired from a long day of work, so if I missed something, please call me out and correct it