Controlling the morphology and crystallographic coherence of assemblies of magnetic nanoparticles is a promising route to functional materials. Time-resolved small-angle X-ray scattering (SAXS) was combined with microscopy and scaling analysis to probe and analyze evaporation-induced assembly in levitating drops and thin films of superparamagnetic iron oxide nanocubes in weak magnetic fields. We show that assembly of micrometer-sized mesocrystals with a cubic shape preceded the formation of fibers with a high degree of crystallographic coherence and tunable diameters. The second-stage assembly of aligned cuboidal mesocrystals into fibers was driven by the magnetic field, but the first-stage assembly of the oleate-capped nanocubes was unaffected by weak magnetic fields. The transition from 3D growth of the primary mesocrystals to the second stage 1D assembly of the elongated fibers was related to the size and field dependence of isotropic van der Waals and directional dipolar interactions between the interacting mesocrystals.