When you guys weigh cases what do you deem as acceptable for variation? Please use percentage as every cartridge case has different weights.
I use a bell curve. Dependent on your intended use, from benchrest to general purpose plinking, and everything in between... you will have light, heavy and those that fall in between. Cull the lights and heavies and use the ones in the middle. The acceptable range is again, up to the intended use.
Also, does variation in bullet tension/pull typically show up through vertical stringing and velocity variation?
Yes. Consistent case neck wall thickness, thru the use of a hand held neck turning lathe along with the use of bushing dies are the best way to obtain consistent neck tension and repeatable neck expansion.
For a standard, production chamber... determine the thinnest case neck wall thickness you will be using, and turn all cases to that value +/- .0005".
Don't over do it if you have a chamber on the large side of a production spec... as you will needlessly stretch the neck. Should the difference in an unturned loaded round and the estimated chamber neck dimension be greater that .006", I recommend not turning the necks.
Instead, try to find a brand of case with a thicker neck wall, which can be turned and still maintain a reasonable maximum clearance, or a case brand with no more than .0005" wall thickness difference.
For benchrest rifles with tight neck chambers... this is all information you would already know, and be putting to use.
I can provide additional information in greater detail, but as it's extensive, I'd provide it in a PM.