The magnetic anisotropy determines the equilibrium orientation of the magnetization in a ferromagnet. In Mn-based inverse tetragonal Heusler compounds, a large uniaxial anisotropy makes these materials excellent candidates for both spin-transfer-torque and skyrmionic devices. Here, we present systematic investigations of the magnetocrystalline anisotropies in MnxPtSn films (x = 1.0-1.6). We find that the MnxPtSn films, grown by magnetron sputtering on MgO substrates, show a structural transition between x = 1.0 and 1.2 from cubic to tetragonal, where the tetragonal structure shows a twinned in-plane c-axis orientation. From ferromagnetic resonance measurements, we determine the out-of-plane and in-plane uniaxial anisotropies, taking into account the particular structural properties of the films. We find a strong dependence of the uniaxial anisotropies on the Mn concentration, as well as on structural distortions due to the lattice-matched growth. From temperature-dependent ferromagnetic resonance measurements, we infer the evolution of the in-plane uniaxial anisotropy and observe the presence of additional magnetic interactions and magnetization relaxation mechanisms around the spin reorientation transition.