The Mass of the mouthpiece refers to it's overall weight.
The weight is determined by the outside shape and type of materials used in the construction.
The internal dimensions of the trumpet air column (including the mouthpiece) set up the resonance characteristics or Harmonic Series of the trumpet.
The trumpet wall to include the material, weight, thickness, heat-treating, stress relieving, or annealing will not affect the Harmonic Series of the trumpet but it can effect how those overtones are amplified.
These properties will have an impact on the amplification of the partials created by the trumpet air column . The bright (upper partials) or dark (lower partials) description is a result of the way these partials are amplified.
Some players feel the added mass helps balance the horn.
That being said, a heavier mouthpiece may help some players slot notes, while other players benefit from lighter blanks. Heavy model mouthpieces in the past have been used to help poorly designed mouthpieces slot slightly better. Some players may find increased projection as well.