ABSTRACTWe investigate the presence of ionized gas outflows in a sample of 141 main-sequence star-forming galaxies at 1.2 < z < 2.6 from the KLEVER (KMOS Lensed Emission Lines and VElocity Review) survey. Our sample covers an exceptionally wide range of stellar masses, 8.1 < log (M⋆/M⊙) < 11.3, pushing outflow studies into the dwarf regime thanks to gravitationally lensed objects. We stack optical rest-frame emission lines (H β, [O iii], H α, and [N ii]) in different mass bins and seek for tracers of gas outflows by using a novel, physically motivated method that improves over the widely used, simplistic double Gaussian fitting. We compare the observed emission lines with the expectations from a rotating disc (disc + bulge for the most massive galaxies) model, whereby significant deviations are interpreted as a signature of outflows. We find clear evidence for outflows in the most massive, log (M⋆/M⊙) > 10.8, AGN-dominated galaxies, suggesting that AGNs may be the primary drivers of these gas flows. Surprisingly, at log (M⋆/M⊙) ≤ 9.6, the observed line profiles are fully consistent with a rotating disc model, indicating that ionized gas outflows in dwarf galaxies might play a negligible role even during the peak of cosmic star-formation activity. Finally, we find that the observed mass loading factor scales with stellar mass as expected from the TNG50 cosmological simulation, but the ionized gas mass accounts for less than 2 ${{\ \rm per\ cent}}$ of the predicted value. This suggests that either the bulk of the outflowing mass is in other gaseous phases or the current feedback models implemented in cosmological simulations need to be revised.