Black powder is measured by weight. It is usually purchased in one pound cans. Pounds, grains and grams are units of weight or mass. One grain equals the weight of one grain of barley if I am not mistaken. 7000 grains to a pound. 15.4 grains to a gram. Different BP granulation will yield different weights by volume. As will the same granulation by different manufacturers. BP charge measures, the brass or plastic tubes with marks on the sides to measure BP, does measure volume but it is calibrated to a certain weight of a consistent substance. Most are calibrated to the volume of grains (weight) of water, specific gravities and what not. The 100 tick mark will be 100 grains (weight) of water. Water will yield the same weight per volume consistently, BP will not. That is especially true for larger granulation. Measures from different manufacturers are different as well.
4f will weigh more than 3f of the same volume because it is a smaller granulation and more dense. 4f burns faster and is more energetic than 3f, resulting in higher pressure. In a gun, you pack the powder down with a ramrod anyway, so original measured volume would be meaningless as it changes when packed, the weight stays the same. Yeah a rocket is not a gun but that doesn't change grain and grams to volume instead of weight.
Volume is measured with milliliters or cubic something. Nowhere will you find a volume measurement of grain or gram. A grain is a grain and a gram is a gram no matter what you are measuring. What weights more, 100 grams of aluminum or 100 grams of lead? Neither. Which occupies the most space? The aluminum, it is less dense. 1 cubic inch of aluminum weighs 682.5 grains. Lead is 2870 grains.
What sort of device are you guys using to measure the "volume" of your BP?
This is why BP is not measured by volume:
https://www.skylighter.com/fireworks/help/Black_Powder_Size_Charts.asp There is quite a bit of variation in the sizes of the grains.
To the OP, here is video showing side by side reactions from different grain sizes. Not really the scientific answer you were looking for, but it will give you an idea of how much more energetic 4f is than 3f. You will notice he uses a scale to measure the BP, not the cup he has it in. Then you will see how much more dense the finer grain powder is, even if it weighs the same.
[video=youtube;WcVlc2m4a1s]https://www.youtube.com/watch?v=WcVlc2m4a1s[/video]
You simply cannot accurately measure black powder by volume.
Mike