The physical interpretation of the spectral line polarization produced by the joint action of the Hanle and Zeeman effects offers a unique opportunity to obtain empirical information about hidden aspects of solar and stellar magnetism. To this end, it is important to achieve a complete understanding of the sensitivity of the emergent spectral line polarization to the presence of a magnetic field. Here we present a detailed theoretical investigation on the role of resonance scattering and magnetic fields on the polarization signals of the Ba II D1 and D2 lines of the Fraunhofer spectrum at 4934 and 4554 Å, respectively. We adopt a three-level model of Ba II, and we take into account the hyperfine structure that is shown by the 135Ba and 137Ba isotopes. Despite their relatively small abundance (18%), the contribution coming from these two isotopes is indeed fundamental for the interpretation of the polarization signals observed in these lines. We consider an optically thin slab model, through which we can investigate in a rigorous way the essential physical mechanisms involved (resonance polarization, Zeeman, Paschen-Back, and Hanle effects), avoiding complications due to radiative transfer effects. We assume the slab to be illuminated from below by the photospheric solar continuum radiation field, and we investigate the radiation scattered at 90°, both in the absence and in the presence of magnetic fields, deterministic and microturbulent. We show in particular the existence of a differential magnetic sensitivity of the three-peak Q/I profile that is observed in the D2 line in quiet regions close to the solar limb, which is of great interest for magnetic field diagnostics.