The presence of dust strongly affects the way we see galaxies and also the chemical abundances we measure in gas. It is therefore important to study he chemical evolution of galaxies by taking into account dust evolution. We aim at performing a detailed study of abundance ratios of high redshift objects and their dust properties. We focus on Lyman-Break galaxies (LBGs) and Quasar (QSO) hosts and likely progenitors of low- and high-mass present-day elliptical galaxies, respectively. We have adopted a chemical evolution model for elliptical galaxies taking account the dust production from low and intermediate mass stars, supernovae Ia, supernovae II, QSOs and both dust destruction and accretion processes. By means of such a model we have followed the chemical evolution of ellipticals of different baryonic masses. Our model complies with chemical downsizing. We made predictions for the abundance ratios versus metallicity trends for models of differing masses that can be used to constrain the star formation rate, initial mass function and dust mass in observed galaxies. We predict the existence of a high redshift dust mass-stellar mass relationship. We have found a good agreement with the properties of LBGs if we assume that they formed at redshift z=2-4. In particular, a non-negligible amount of dust is needed to explain the observed abundance pattern. We studied the QSO SDSS J114816, one of the most distant QSO ever observed (z=6.4), and we have been able to reproduce the amount of dust measured in this object. The dust is clearly due to the production from supernovae and the most massive AGB stars as well as from the grain growth in the interstellar medium. The QSO dust is likely to dominate only in the very central regions of the galaxies and during the early development of the galactic wind. Comment: 16 pages, 16 figures, A&A accepted