550b and RCBS rangemaster for spot-checks. I'm sure it's not exact each time +/- 0.1gr, maybe a spherical powder would be more consistent, but I do like the way Varget behaves (and the big pieces are easier to pick up if I spill a couple granules
The amount of powder charge is related to the weight, yes. Volumetric is fairly consistent from charge to charge, but not exact, due to the way the granules stack, etc. Not normally enough to worry about, but if you wanted to be exact, follow the poster above who suggests a light volumetric dispense, then a trickle to the desired weight. The flip-side is that when you dump it into the shell, it's going to fall slightly different each time as well. smaller size granules, or tapping the case (if filling it to a compressible amount) before seating the bullet, can help make more consistent rounds, but that's splitting hairs (along with variances in bullet weight, temperature)...
I used to be very careful with my weights - with the Lee 50 press, I'd make up 100 rounds of 9mm a night, all of them almost exactly the same. These days, I'll do 400-500 rounds in an evening, not exact, but can punch paper the same.