Well, my calibration for weights and caliper came in a couple days ago and I checked my balance and calipers. The calipers is right on.
I massed a series of weights from 1 mg to 5.7 grams and collected data points. I entered them into the solution for a Least Square Linear Regression to determine the function which best matched the data points. Here is the results:
actual mass = 0.999*mass reading + 0.204
Just as I suspected, the scale at the lower end shows a value which is lower than the actual mass, and at the high end of the scale they are much closer together. So, when I was reading "3.9" grains of HP-38 on the scale it was actually 4.1 grains. My "4.0" loads were actually 4.2 grains, which explained why they were so loud, recoil was greater than normal, and the casing was ejected twice as far as my lighter loads or my commercial stuff. If I want 3.9 grain loads I'd have to mass it to 3.7 grains on the scale. What I actually did was mass 10 charges (initially 20 but 10 worked well enough) on the scale and divide by 10 to see what a single charge would mass. I putzed with the 10 charges until my computed single charge was 3.87gr, which was as close as I could get to 3.9 gr. Loading 100 rounds and checking every twenty my 10 charge mass was within 0.1 grains of 38.7 each time, so that is what I am going to continue to do.