For my rifles, I keep the brass to one head stamp. And if it's Rem or Win, I weight sort them. Only for the 223 bolt gun do I have some mixed brass. Most of the 223 brass is segregated by headstamp, but I do have a good supply of mixed mongrel brass, which isn't prepped in any way. So...the point of this is that, when I was shooting groups and testing various resizing dies with all that brass, the groups with the mixed head stamps shot a little worse. For target shooting, the accuracy diff would have been too much, but for hunting purposes it would not have mattered.
So, yes, case weight matters, but maybe not to everyone.