"First contemplation of the problems of Interior Ballistics gives the impression that they should yield rather easily to relatively simple methods of analysis. Further study shows the subject to be of almost unbelievable complexity." Homer Powley
Simple in principle but not in practice. The problem is the bullet is moving when the pressure peak occurs. So, if the timing of the pressure peak isn't exactly the same from one shot to the next, the bullet isn't in the same position from one to the next. That means the expansion of the powder space behind the bullet isn't the same, so the volumes the pressure peaks in aren't the same, and that changes both the pressure peak value, which affects the ballistic efficiency, and with it, the final velocity of the bullet at the muzzle. In a gross comparison, that is why putting the same weight of same energy density fast and slow burn rate powders behind a bullet don't produce the same peak pressure and velocity.
So, whether or not the peak occurs at the same point in bullet travel down the bore depends on the powder burning characteristics being the same from one shot to the next. And that's where the volume vs. weight problem gets its start.
Take a look at the image below. All three are of the same case filled with the same charge; the exact, actual same charge, poured back out and re-filled for each photo. The difference is the first is poured in with a funnel with a short spout. The next has a spout extension (drop tube) a few inches long. The last one has a drop tube three feet long. See how the bulk density is changed?
When the grains are packed more closely together, the flame front and hot gases have a harder time moving between the grains and lighting the powder. The result is a slower starting burn rate in the more dense packing. Hatcher's Notebook (pp. 312-313) has an example of a powder with long grains that could only be dispensed to within a spread of 1.7 grains my the Frankford Arsenal loading equipment producing better accuracy than a similar burn rate short grain powder that could be dispensed within a spread of 0.6 grains. The coarse grain powder apparently self-compensated for its load density when it packed tighter by its starting burn rate being reduced by just the right amount. As a result, if the powder falling into the measure cavity were more densely packed than a previous charge, it could produce about the same barrel time and velocity. The long grains probably also kept the load density structure better locked in place when it was moved around later, especially if the load was slightly compressed.
That example also shows that this property isn't the same for all powders and grain cuts. Some may produce better accuracy by volumetric measure (especially when you are loading at the bench, so this isn't changed much in transport) and some may do better by weight. I find IMR 4064 tends toward being one of the former, as an example, making a great powder measure powder.