Resonance-scattering polarization and the Hanle effect are powerful but seldom exploited probes into the magnetism of the quiet solar atmosphere. They are also very interesting checks of the quantum theory of atomic polarization. The Ba ii D2 line has been known for more than 20 years as presenting a conspicuous signal of resonance scattering polarization thanks to its atomic configuration and the presence of five different isotopes of Ba, two of which present a hyperfine structure.A model that considers most of the known ingredients of the atomic polarization of Ba ii related to the formation of the D2 line was presented in 2007. We intend to observe all the variability of the Stokes profiles of this line in conditions of resonance scattering to verify the general validity of the model and to ascertain the use of the model for magnetic field diagnostics in the quiet solar chromosphere and in spicules. The new CCD cameras at THEMIS and the recently commissioned tip-tilt tracking system gave us the opportunity to perform the required observations with unprecedented precision and reliability, resulting in data ready to confront the present theory.The Stokes Q profiles, both off-limb and on disk, appear to verify this theory in qualitative terms. The observed departures in terms of overall signal amplitude and relative ratios among the three spectral features point to a refinement of the theory for quantitative purposes, perhaps including radiative-transfer effects. We observed, on the other hand, anomalous Stokes V profiles in the absence of Zeeman effect that remain unexplained.The qualitative agreement between the theory and the observations encourages an increased effort to also match the observations from a quantitative point of view, including the observed anomalous Stokes V profiles.