Brass weight is important but bullet weight is crucial. The whole reason I started reloading was because I had trouble finding the same brand and load from year to year. I'd have the gun sighted in for Remington 180 grain and the next year all I could find was Federal 150 grain, that sort of thing. And I didn't have a range nearby, I had to wait to sight in at deer camp...and since I was driving at night to deer camp, that meant I had to hunt with a load the next morning that might or might not be sighted it. Or I might have to hunt with an assortment of loads that didn't all have the same point of impact. This was back before the days of Midway of course.
Getting started was not easy back then. But I finally rounded up what I needed to reload, bought a large batch of military surplus 30-06 and pulled the bullets and I started loading from that batch of brass and used the same bullet and load for over a decade. And like magic I started making one shot kills.