If I want really accurate ammo, I weigh brass, bullet and powder. Setting aside brass, velocity is a function of how much powder and how much bullet. Take, for example, a .223 load I'm working on.
The powder charge is 25gr. Most of us probably weigh our powder to -+.1gr - in this case a .8% tolerance. The bullet weight is 55gr (actual average is 55.5gr). I'm using bulk pack remington bullets, which have a extreme variance of up to 3gr in either direction (a 5.5% variance). About 75% fall within .3gr of the average 55.5gr (about a 1.1% variance) - these are the ones I use for super accurate loads. I use the leftovers for "practice grade" ammo. It just doesn't make sense to hold the powder to about 1% and not do the same with the bullets.
Just a guess at what might happen if I didn't weigh my bullets: Most rounds would group tight - but an occasional round with a heavy or light bullet would result in a "flyer" outside the group. I would probably blame myself and not even think it was the ammo.
Just my $ .02 worth....