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For sculpts, with the exception of an edge case at density 0 making the sculpt near massless, the relationship between the value of the density tweak and the mass is exponential:
mass = 1000kg * volume in m³ * e ^ (6 * density + 2.96867907)
But for puppets, it's different. After overcoming the initial confusion of the puppet losing a small amount of mass while it's being held with R2, I worked out that the relationship between the puppet's scale and its mass was cubic as expected. But I haven't yet been able to work out the relationship between its collision capsule width, its density, and its mass. As with the sculpt, the density appears to have an edge case at 0 - but nowhere near as extreme as the one for the sculpt. Also, the density-mass curve is neither linear nor exponential - perhaps a polynomial?
As for why I'm interested in this. I have a puppet in a group, and its transform relative to the group is keyframe animated. But that makes it contribute zero mass to the group, so I'm experimenting with adding a puppet equivalent mass proxy sculpt to the group, and I'm trying to set up a network of calculators between the puppet and the sculpt to give the sculpt the correct mass.