We study the relation between the microscopic structure and dynamics and the macroscopic rheological response of glass-forming colloidal suspensions, namely binary colloidal hard-sphere mixtures with large size asymmetry (1:5) that span a large range of mixture compositions close to the glass transition. The dynamical shear moduli are measured by oscillatory rheology and the structure and dynamics on the single-particle level by confocal microscopy. The data are compared with Brownian Dynamics simulations and predictions from mode-coupling theory based on the Percus-Yevick approximation. Experiments, simulations and theory consistently observe a strong decrease of the intermediate-frequency mechanical moduli combined with faster dynamics at intermediate mixing ratios and hence a non-monotonic dependence of these parameters but a localization of the large particles which decreases monotonically as the fraction of small particles is increased. We find that the Generalized-Stokes Einstein relation applied to the mean square displacements of the two components leads to a reasonable estimate of the shear moduli of the mixtures and hence links the rheological response to the particle dynamics which in turn reflects the microscopic structure. © 2019 The Royal Society of Chemistry.