We investigate the role of stellar mass in shaping the intrinsic thickness of galaxy discs by determining the probability distribution of apparent axial ratios (b/a) for two different samples that probe the faint end of the galaxy luminosity function. We find that the b/a distribution has a characteristic `U-shape' and identify a limiting mass M* ~ 2 × 109Msolar below which low-mass galaxies start to be systematically thicker. This tendency holds for very faint (MB ~ -8) dwarfs in the local volume, which are essentially spheroidal systems. We argue that galaxy shape is the result of the complex interplay between mass, specific angular momentum and stellar feedback effects. Thus, the increasing importance of turbulent motions in lower mass galaxies leads to the formation of thicker systems, a result supported by the latest hydrodynamical simulations of dwarf galaxy formation and other theoretical expectations. We discuss several implications of this finding, including the formation of bars in faint galaxies, the deprojection of HI line profiles and simulations of environmental effects on the dwarf galaxy population.