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Context. Planetesimal belts are ubiquitous around nearby stars, and their spatial properties hold crucial information for planetesimal and planet formation models. Aims. We present resolved dust observations of 74 planetary systems as part of the REsolved ALMA and SMA Observations of Nearby Stars (REASONS) survey and archival reanalysis. Methods. We uniformly modelled interferometric visibilities for the entire sample to obtain the basic spatial properties of each belt, and combined these with constraints from multi-wavelength photometry. Results. We report key findings from a first exploration of this legacy dataset: (1) Belt dust masses are depleted over time in a radially dependent way, with dust being depleted faster in smaller belts, as predicted by collisional evolution. (2) Most belts are broad discs rather than narrow rings, with much broader fractional widths than rings in protoplanetary discs. We link broad belts to either unresolved substructure or broad planetesimal discs produced if protoplanetary rings migrate. (3) The vertical aspect ratios (h=H/R) of 24 belts indicate orbital inclinations of ~1–20º, implying relative particle velocities of ~0.1–4 km/s, and no clear evolution of heights with system age. This could be explained by early stirring within the belt by large bodies (with sizes of at least ~140 km to the size of the Moon), by inheritance of inclinations from the protoplanetary disc stage, or by a diversity in evolutionary pathways and gravitational stirring mechanisms. We release the REASONS legacy multidimensional sample of millimetre-resolved belts to the community as a valuable tool for follow-up multi-wavelength observations and population modelling studies.