There are two aspects of this: the geometry of solder particle packing... and some things we can lump together under the heading of "harsh realities".
Just from a theoretical point of view (monodisperse powder diameter / perfectly spherical particles), the maximum volume that can be occupied by these particles is 0.740. This is the so-called "maximum packing fraction". You can prove this yourself by taking a triangular prism as a unit repeating cell and calculating the volume of fractional-spheres inside it - see the picture for the two ways that hexagonally-close-packed spheres can be arranged - the math is easier for the A-B-A packing. Note that this is [I}independent of the diameter of the particles[/I], which is counter-intuitive, but nonetheless correct. In other words, no matter how small the particles are, you should always be able to get them to achieve a maximum volume fraction of 0.74.
For randomly-arranged spheres, the maximum packing fraction is usually agreed to be somewhere between 0.67-0.69. Of course, at the maximum fraction, any solder paste would just be a solid mass, and the typical volume fraction of a solder paste is from 0.4 to 0.54 by volume of solder (from 75-93%w/w powder, depending on the alloy and the application).
So to achieve the same viscosity needed for the application, you need less volume of solder powder, and hence less % by weight, if the powder is more monodisperse.
Theory is nice, but we'll talk about the "harsh realities" of solder paste in the next post.