Galaxy properties are known to correlate most tightly with the galaxy effective stellar velocity dispersion $sigma_{rm e}$. Here we look for {em additional} trends at fixed $sigma_{rm e}$ using 1339 galaxies ($M_ast gtrsim 6times10^9$ M$_odot$) with different morphologies in the MaNGA (DR14) sample with integral-field spectroscopy data. We focus on the gradients ($gamma_{rm rms} equiv sigma(R_{rm e}/4)/sigma_{rm e}$) of the stellar root-mean-square velocity ($V_{rm rms} equiv sqrt{V^2 + sigma^2}$), which we show traces the total mass density gradient $gamma_{rm tot}$ derived from dynamical models and, more weakly, the bulge fraction. We confirm that $gamma_{rm rms}$ increases with $sigma_{rm e}$, age and metallicity. We additionally find that these correlations still exist at fixed $sigma_{rm e}$, where galaxies with larger $gamma_{rm rms}$ are found to be older and more metal-rich. It means that mass density gradients contain information of the stellar population which is not fully accounted for by $sigma_{rm e}$. This result puts an extra constraint on our understanding of galaxy quenching. We compare our results with galaxies in the IllustrisTNG hydrodynamical simulations and find that, at fixed $sigma_{rm e}$, similar trends exist with age, the bulge fraction, and the total mass density slope but, unlike observations, no correlation with metallicity can be detected in the simulations.