There is correlation between weight and capacity with some lots of some cartridges. I've seen it, and I've seen otherwise.
Matching weight itself can be difficult given your case preps. For me, I'm setting primer pocket depths, turning necks, chamfering mouths, trimming settled necks w/resp to or within 5thou of chamber end, which is hopefully by 3rd FFing, re-chamfering.
I've invested money/time in the prepped cases before I could cull by weight, and then I would wonder with each what their capacity really is anyway. Would 20 cases separated as matching in weight actually match in capacity? Would there be a few that don't? Are any of 5 pulled out for weight departure actually matching capacity of the 20 group?
Hell I might as well just measure capacities. It's the only way to know.
I'm also calibrating QuickLoad for gun, which I need accurate capacity for anyway.
What varies capacities of cases weighing the same, even if webs/heads match in form, and all preps completed, is case spring backs. They're tapered in thickness from webs to mouths, varying of course, which varies spring back from up/down sizing (reload cycles). The more you size this variance the greater the variance grows. Throw partial length annealing in there, maybe it isn't precise,, that won't help in capacity matching. Using the brass at different pressures during load development, leads to more/less sizing of that brass in the same dies. Different hardening for spring back changes.
I've been matching capacities a long time. There is no shortcut, and I toss a significant percentage of brass with it. I use custom chambers and dies, and I choose smaller improved cartridges that are viable for this. 260AI over 6.5x284 (for example), and forget about it with something like a 264wm, or a 30-06..
The only reason to match capacities is for long term accuracy, and that includes a plan that allows long term use of brass (which you would invest so much into).
IMO, the only value in weighing cases is in finding problems. X lot weighs way more/less than Y lot. 7 out of 4,000 had missing flash holes or mutated case heads. If you write all these weights down, you're still a long way from grouping anything by capacities. So if not willing to go through the efforts of actual capacity measure & management, maybe it's not viable to do so, you can still weigh cases.
Just don't assign excess credit for that.