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The evolution of the dust grain size distribution has been studied in recent years with great detail in cosmological hydrodynamical simulations taking into account all the channels under which dust evolves in the interstellar medium. We present a systematic analysis of the observed spectral energy distribution of a large sample of galaxies in the local Universe in order to derive not only the total dust masses but also the relative mass fraction between small and large dust grains (DS / DL). Simulations reproduce fairly well the observations except for the high-stellar mass regime where dust masses tend to be overestimated. We find that ∼45 per cent of galaxies exhibit DS / DL consistent with the expectations of simulations, while there is a subsample of massive galaxies presenting high DS / DL (log (DS / DL) ∼ −0.5), and deviating from the prediction in simulations. For these galaxies which also have high-molecular gas mass fractions and metallicities, coagulation is not an important mechanism affecting the dust evolution. Including diffusion, transporting large grains from dense regions to a more diffuse medium where they can be easily shattered, would explain the observed high DS / DL values in these galaxies. With this study, we reinforce the use of the small-to-large grain mass ratio to study the relative importance of the different mechanisms in the dust life cycle. Multiphase hydrodynamical simulations with detailed feedback prescriptions and more realistic subgrid models for the dense phase could help to reproduce the evolution of the dust grain size distribution traced by observations. [ABSTRACT FROM AUTHOR]