Context. Among the spectroscopically identified white dwarfs, a fraction smaller than 2% have spectra dominated by carbon lines, mainly molecular C2, but also a smaller group dominated by C I and C II lines. These are together called DQ white dwarfs. Aims. We want to derive atmospheric parameters Teff, log g, and carbon abundances for a large sample of these stars and discuss implications for their spectral evolution. Methods. Sloan Digital Sky Survey spectra and ugriz photometry were used, together with Gaia Data Release 2 parallaxes and G band photometry. These were fitted to synthetic spectra and theoretical photometry derived from model atmospheres. Results. We found that the DQ hotter than Teff ~ 10 000 K have masses ~ 0.4 M⊙ larger than the classical DQ, which have masses typical for the majority of white dwarfs (~ 0.6 M⊙). We found some evidence that the peculiar DQ below 10 000 K also have significantly larger masses and may thus be the descendants of the hot and warm DQ above 10 000 K. A significant fraction of the hotter objects with Teff > 14 500 K have atmospheres dominated by carbon.