I am with Bill. Weighing brass doesn't really matter BECAUSE you are not measuring what does matter and that is case volume.
The goal in making precision ammo is to make each rd identical. We want each bang to produce the same barrel harmonics which equates to pressure (time and curve) and velocity. We also want that bullet to be true with the bore.
Case volume and brass ductility is critical to that consistency. When shooters weigh brass, they assume that the exterior machining is the same so any difference in weight relates to case volume. Not true.
Simple differences in machining the extractor groove can lead to enough weight difference to cull that brass. Tells you nothing.
So measure the case volume. Quick and easy to do with fire formed and trimmed brass that is not sized. Take a very fine ball gunpowder. I use Win680. Fill a case to the brim tapping to make sure as much as possible goes in. Dump into another case and repeat. If any case shows more or less volume, mark and test fire. Good chance it will not shoot well - garbage time.
In general, I have found cases that didn't weigh the same but had the same case volume and shot very well.
Annealing is next as you want that neck to expand the same amount and rate during fire. Plus that leads to consistent neck tension. All good things.
The biggest benefit you can do to make a more accurate rifle, monitor the runout of your ammo. If runout over a few thou is introduced in your ammo during the sizing or seating, all the brass prep in the world will not produce good ammo. That bullet must engrave in those lands true.
Runout or wobble will put the tip in any direction but straight down the bore. Traveling cockeyed down the bore usually doesn't lead to a true flight to the target.
There are a ton of little tweaks that can be done to improve LR accuracy and each rifle will need its own share of tuning.
www.6mmbr.com has lots of very interesting posts from some of the top shooters in the LR game.
Weigh the brass if that makes you happy but also check the volume. I bet the results will surprise you.
Jerry
PS don't be afraid of Domestic Commercial brass. Many are using this in top US competitions and winning. I have used all the common brands with superb results. I actually don't like Norma as it is very soft in the cartridges I have tested.