We report a detailed investigation of RECoPO (RE = La, Pr) and LaCoAsO materials performed by means of muon spin spectroscopy. Zero-field measurements show that the electrons localized on the Pr$^{3+}$ ions do not play any role in the static magnetic properties of the compounds. Magnetism at the local level is indeed fully dominated by the weakly-itinerant ferromagnetism from the Co sublattice only. The increase of the chemical pressure triggered by the different ionic radii of La$^{3+}$ and Pr$^{3+}$, on the other hand, plays a crucial role in enhancing the value of the magnetic critical temperature and can be mimicked by the application of external hydrostatic pressure up to 24 kbar. A sharp discontinuity in the local magnetic field at the muon site in LaCoPO at around 5 kbar suggests a sizeable modification in the band structure of the material upon increasing pressure. This scenario is qualitatively supported by emph{ab-initio} density-functional theory calculations.
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