We report results of a spectropolarimetric and photometric monitoring of the weak-line T Tauri stars (wTTSs) V819 Tau and V830 Tau within the MaTYSSE (Magnetic Topologies of Young Stars and the Survival of close-in giant Exoplanets) programme, involving the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope. At similar or equal to 3 Myr, both stars dissipated their discs recently and are interesting objects for probing star and planet formation. Profile distortions and Zeeman signatures are detected in the unpolarized and circularly polarized lines, whose rotational modulation we modelled using tomographic imaging, yielding brightness and magnetic maps for both stars. We find that the large-scale magnetic fields of V819 Tau a...