Grain growth (GG), mediated by grain boundary (GB) migration, is a fundamental mechanism of microstructure evolution in polycrystalline materials. GB migration is frequently accompanied by a relative shear displacement of grains meeting at GBs, a phenomenon known as shear-coupling. This coupling induces internal stresses within the microstructure, which recent studies have shown to play a decisive role in dictating microstructure evolution and GG pathways. This work provides a detailed characterization of the statistical features of two-dimensional GG in the presence of GB shear-coupling through continuum modeling of GB migration that incorporates fundamental microscopic mechanisms and diffuse-interface simulations. We demonstrate that incorporating shear-coupling produces a more heterogeneous, less equiaxed microstructure than conventional curvature-driven GG, while yielding topological and geometric properties consistent with experimental and atomistic observations. We further demonstrate that as grain grows in this regime, internal stress relaxes. Highly stressed grains shrink faster, and lightly stressed grains grow faster than other grains. These findings demonstrate that internal stress, an intrinsic feature of GG, profoundly changes essential features of GG microstructure and kinetics, consistent with experiments and atomic-scale simulations. Moreover, we discuss their implications for GG regimes and scaling behavior.