It's not so much about weighing cases but ensuring consistency in your brass.
Don't mix brass. Every maker makes them to certain specifications. Some may thicker or heavier than others. Some have slightly higher capacity than others.
So, buy your stuff brand new, say five boxes of twenty cartridges. Keep them and reload them as a group. Log it.
If you have another lot, keep them separate and treat them separate. You can reload them the same way (especially if they shoot well for your gun), but their service life will be different from another lot/group.
Vigilantibus et non dormientibus jura subveniunt. Molon Labe!