About three years ago I weight sorted a bunch of ammo. I then divided each type of ammo into two groups. One group had the weights matched to the tenth of a grain for each target shot (WM - Weight Matched), while the other group were paired to give the most extreme weight difference (MO - Matched Outliers). I then shot the groups of each and compared results.
Overall with all ammo types lumped together, group size went down 9% for the weight matched, compared to the matched outliers, and there was statistical evidence (TTEST) that there was a difference between the two groups.
However, if you look at the detail, and I've included the results below in a table, you will see that the ammo types which showed improvement (highlighted in green) were the ones which shot the poorest. There was one anomaly in the results, for Eley Practice (highlighted in yellow). It showed statistical significance of a difference, but the weight matched group shot poorer than the matched outliers.
In the best quality ammo it did very little if anything. This is not surprising. For example the Lapua Midas M all weighed the same +/- 0.05 grains. There essentially was no way to weight sort them because they were the same weight to start will.
My conclusion is that it may be of a minor help to poor quality ammo, but it is still going to shoot poorly even weight sorted. I think the bottom line is that good quality ammo will likely be very consistent in weight. However if you make poor quality ammo consistent in weight it does not turn a sow's ear into a silk purse. The issue is that each sub component needs to be the same, not just the total. That is what quality ammo is about; same brass weight, same primer weight, same powder weight, and same bullet weight, not just the total. I have not bothered to weigh ammo again.
Hope that helps some,