Bager,
I actually check my weight AFTER the dive on a lot of dives, at least once a trip, sometimes more if I have new equipment or in a new diving situation. If I am diving an unknown, I take my best guess based on similar dives from my logbook and maybe add a couple of pounds and go diving.I am almost always within a couple of pounds this way. I put some of the weights into my BC pockets and at the end of the dive while waiting for the rest of the divers to exit the water, I can check my bouyancy, removing weights from my pockets and handing them to my buddy as necessary. After figuring out the correct weight, it gets logged with all the details, water, wetsuit ,ect,ect. It does not take too many dives to build yourself a good guide for you. If nothing else, it gives me something to do while waiting for the ladder to clear.
As for the neutral at 15 ft, there seems to be 2 schools of thought on this. One says to be neutral at 15 ft and the other at the surface, both of which with about 500 psi remaining. I prefer the surface to be neutral at. If you are neutral at 15 ft with an empty BC, a low tank and any sort of wetsuit at all, you will be positive above 15 ft and the only way to stop an uncontrolled accent is finning. I don't like having a zone in which I have to fight to keep control.
I suspect the "secret" is just experience. After getting a lot of new divers geared up, it should not be too hard for an experienced instructor to make a educated guess at what a diver should need.