Progress in advanced fuels and waste forms requires unprecedented control of the design and organization of systems at the micro, meso, and nanoscale. In the last years, weberite-type oxides with the general formula A3BO7 (where A is a trivalent rare earth element and B is a pentavalent cation, such as Ta, Nb) have sparked interest in a number of technological applications due to their chemical and structural flexibility, which leads to a broad spectrum of physical properties, such as high ionic conductivity, ferroelectricity, and photocatalytic activity. In addition, weberite-type oxides have recently been linked to pyrochlore oxides (A2B2O7) because they share similar atomic building blocks that form after exposure to swift heavy ions. Here, we present a comprehensive ion irradiation study on weberite-type tantalate oxides (A3TaO7, A = Pr, Tb, Dy, Y, Yb), covering three major structural classes characterized by different long-range symmetries and organizations at the nano and mesoscale. Irradiation experiments were performed using 1.6 GeV Au ions at the X0 beamline of the GSI Helmholtz Center (Darmstadt, Germany). Samples were analyzed using the neutron total scattering technique at the Nanoscale-Ordered Materials (NOMAD) beamline at Oak Ridge National Laboratory and X-ray diffraction at the Advanced Photon Source (APS) at Argonne National Laboratory, respectively. The data analysis establishes a link between the material resistance to amorphization and the A-site cation ionic radius: smaller cations enhance radiation resistance to amorphization. Analyses of the neutron pair distribution function (PDF) establish that the pristine (unirradiated) local organization in these materials is a critical factor: indeed, ion beams are more susceptible to destroying the long-range order in orthorhombic Pr3TaO7 (Cmcm) than in Tb3TaO7 (Ccmm). Cubic Yb3TaO7 (an Fm-3m oxygen-deficient fluorite) does not display any long-range organization of the cations and vacancies though it does at the nanoscale: this system shows the highest radiation resistance and only extremes radiation levels trigger, besides a minor amorphization, the transformation another cubic structure, which was previously reported only during swift heavy ion irradiation of lanthanide sesquioxides (A2O3).