  We investigate the entanglement, CHSH nonlocality, fully entangled fraction
and symmetric extendibility of two-qubit states that have a single maximally
mixed marginal. Within this set of states, the steering ellipsoid formalism has
recently highlighted an interesting family of so-called 'maximally obese'
states. These are found to have extremal quantum correlation properties that
are significant in the steering ellipsoid picture and for the study of
two-qubit states in general.
