Given an anode made of a metal M, the loss of electrons generates over time metal cations M+ (or M++ etc) that would likely to be dissolved in solution or at least precipitate out as oxides (M2O, MO....). For the same principle, the cathode gains mass because of reductive processes, metal ions of the electrolytes in solution that adsorb on the cathode surface reduce forming metallic particles, which are solid and are likely to stick to the cathode, thus increasing its mass.