We studied the stellar populations of 40 early-type galaxies using medium-resolution long-slit spectroscopy along their major axes (and along the minor axis for two of them). The sample, including elliptical and lenticular galaxies as well as dwarf galaxies, is combined with other previously published data in order to discuss the systematics of the radial gradients of age and metallicity over a large mass range, from 107 M&sun; to 1012 M&sun; (-9.2 > MB > -22.4 mag). The well-known mass-metallicity relation is continuous throughout the whole mass range, in the sense that more massive galaxies are more metal-rich. The age-mass relation is consistent with the idea of downsizing: smaller galaxies have more extended star formation histories than more massive ones. The transition-type dwarfs (intermediate between dwarf irregular and dwarf elliptical galaxies) deviate from this relation having younger mean age, and the low-mass dwarf spheroidals have older ages, marking a discontinuity in the relation, possibly due to selection effects. In all mass regimes, the mean metallicity gradients are approximately -0.2 and the mean age gradients +0.1 dex per decade of radius. The individual gradients are widely spread: -0.1 < ∇Age < 0.4 and -0.54 < ∇[Fe/H] < +0.2. We do not find evidence for a correlation between the metallicity gradient and luminosity, velocity dispersion, central age or age gradient. Likewise, we do not find a correlation between the age gradient and any other parameter in bright early-type galaxies. In faint early-types with MB≳-17 mag, on the other hand, we find a strong correlation between the age gradient and luminosity: the age gradient becomes more positive for fainter galaxies. Together with the observed downsizing phenomenon this indicates that, as time passes, star formation persists in dwarf galaxies and becomes more centrally concentrated. However, this prolonged central star formation is not reflected in the metallicity profiles of the dwarfs in our sample. We conclude that various physical mechanisms can lead to similar gradients and that these gradients are robust against the environmental effects. In particular, the gradients observed in dwarf galaxies certainly survived the transformation of the progenitors through tidal harassment or/and ram-pressure stripping. The diversity of metallicity gradients amongst dwarf elliptical galaxies may reflect a plurality of progenitors' morphologies. The dwarfs with steep metallicity gradients could have originated from blue compact dwarfs and those with flat profiles from dwarf irregulars and late-type spirals.