There is no way to even tell what the deviation you are weighing. Erratic velocity is going to cause the biggest issue in group size, but the is no way to know if you are sorting by powder charges, priming compound, bullet weight, or a thick case. Basically buy better ammo if better consistency is needed.
This. This is Science 101. When conducting a simple experiment, you test only one variable at a time, while holding all others constant. Can't do this with an intact cartridge. As a proportion of the overall weight, the bullet is the heaviest component. A certain variation in the bullet weight will have less effect than the same variation in the powder. This can't be determined by weighing an entire cartridge. OTOH, weighing and comparing batches of cartridges
could determine which has the least variation which
might affect relative accuracy.
All of that said, the greatest variation is going to be the shooter and the wind. What to do? Study and improve your technique. Buy the best ammo you can afford and learn to read the wind, preferably with good wind flags. Keep good notes.
Have fun.
Added: As a RSO, I can't begin to relate how often I have watched shooters "testing" high end equipment: rifles, scopes, ammo while employing poor technique or shooting from a less than stable rest and/or shaky bench.
