We present the results of a study of stellar population properties at large galactocentric radii of 14 low-mass early-type galaxies in the Fornax and Virgo clusters. We derive radial profiles of age, total metallicity [Z/H] and [α/Fe] abundance ratios out to ∼1–3 effective radii by using nearly all of the Lick/IDS absorption-line indices in comparison to recent single stellar population models. We extend our study to higher galaxy mass via a novel literature compilation of 37 early-type galaxies, which provides stellar population properties out to one effective radius. We find that metallicity gradients correlate with galactic mass, and the relationship shows a sharp change in slope at a dynamical mass of ∼3.5 × 1010 M⊙. The central and mean values of the stellar population parameters (measured in r≤re/8 and at r=re, respectively) define positive mass trends. We suggest that the low metallicities, almost solar [α/Fe] ratios and the tight mass–metallicity gradient relation displayed by the low-mass galaxies are indicative of an early star-forming collapse with extended (i.e. ≥1 Gyr), low-efficiency star formation, and mass-dependent galactic outflows of metal-enriched gas. The flattening of metallicity gradients in high-mass galaxies and the broad scatter of the relationship are attributed to merger events. The high metallicities and supersolar abundances shown by these galaxies imply a rapid, high efficiency star formation. The observed [Z/H]–mass and [α/Fe]–mass relationships can be interpreted as a natural outcome of an early star-forming collapse. However, we find that hierarchical galaxy formation models implementing mass-dependent star formation efficiency, varying initial mass function, energy feedback via active galactic nucleus and the effects due to merger-induced starbursts can also reproduce both our observed relationships.