We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO3, FeBO3, CoCO3, and NiCO3. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified ``toy model{''} to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.