  We study the magnetic-field dependence of Landau levels in graphene
proximitized by large spin-orbit coupling materials, such as transition-metal
dichalcogenides or topological insulators. In addition to the Rashba coupling,
two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and
staggered (valley Zeeman type), are included, to resolve their interplay with
magnetic orbital effects. Employing a continuum model approach, we derive
analytic expressions for low-energy Landau levels, which can be used to extract
local orbital and spin-orbit coupling parameters from scanning probe
spectroscopy experiments. We compare different parameter regimes to identify
fingerprints of relative and absolute magnitudes of intrinsic spin-orbit
coupling in the spectra. The inverted band structure of graphene proximitized
by WSe$_2$ leads to an interesting crossing of Landau states across the bulk
gap at a crossover field, providing insights into the size of Rashba spin-orbit
coupling. Landau level spectroscopy can help to resolve the type and signs of
the intrinsic spin-orbit coupling by analyzing the symmetry in energy and
number of crossings in the Landau fan chart. Finally, our results suggest that
the strong response to the magnetic field of Dirac electrons in proximitized
graphene can be associated with extremely large self-rotating magnetic moments.
