I'll go along with most of what these knowledgeable fellows have to say but will disagree with a fine point.
First off, if you are lucky enough to have a rifle chambered with a reamer on its last few cuts and therefore being chambered to the minimum spec side, it likely won't make much difference to your hunting groups.
As an example, I have a T3 in 6.5x55 that just doesn't care what you shoot through it. At 200 meters, it will shoot the offerings of the same bullet weight from four different manufacturers into a consistent 4cm or 2in. Each will be in a 1in cluster as per manufacturer. The other T3 I have, is a whole different bird. Try six inch groups at 200 yards with different manufacturers.
The only difference between these rifles, is the chamber. The latter rifle has a slightly larger chamber.
As for different brands or lots of cases shooting into different groups. Maybe. It depends on lots of things. The main thing isn't so much weight but the distribution of that weight. Starting off with cases of the same make and lot number saves a lot of time and like mentioned previously works well. Buying large quanties and sorting them into weight batches is very effective and makes for consistent ammo.
If you want to get really picky, trim each case to length, add a primer and weigh it, fill it with water, until the miniscus is level with the case mouth and fill it again. This will give you the true volumetric capacity of the case. This, if you are being anal about constants, is what you are really trying to determine. This can be measured in any form you like, as long as it's repeatable and accurate.
If volumetric capacities are within certain parameters, your velocities and accuracy will be good with similar loads.
I used to be extremely anal about such things, when I was shooting Hunter Bench Rest. I measured every case by volume. Now, I just do what Ganderite does, only not on such a grand scale. I also fireform my brass and neck resize only, then mark the storage boxes for the individual rifles they are sized for.
For most people, that is still far to anal but hitting a game animal properly is at least as important and maybe more so than a super tight group on a target.
Now, another thing to take into account, are bullets, primers and powder. Are they all from the same lot??? Some lots of bullets, just aren't as accurate as others. Today, with the use of Juenke gauges by manufacturers, bullet jackets are more consistent than ever. Almost match grade, even for cheaper types.
Powder, can and does vary lot for lot. Like Ganderite and his large brass purchases, I buy powder in eight pound kegs When I get down to 4 pounds, I buy another eight pound keg and mix all twelve or so pounds together as a blend. This works very well and there is little to no difference from one batch to the next. I have had some real surprises though.
Case preparation is a good place to start.
If all you can afford or have access to is mixed bags of cases, don't be to concerned. Separate them by weight, before pulling the primers, check their weights by water volume and pick the cases that are similar.
Once you've done this, reanneal the cases and fireform them in your rifle.
