van der Waals density functional theory is integrated with analysis of a non-redundant set of protein-DNA crystal structures from the Nucleic Acid Database to study the stacking energetics of CG:CG base-pair steps, specifically the role of cytosine 5-methylation. Principal component analysis of the steps reveals the dominant collective motions to correspond to a tensile "opening" mode and two shear "sliding" and "tearing" modes in the orthogonal plane. The stacking interactions of the methyl groups globally inhibit CG:CG step overtwisting while simultaneously softening the modes locally via potential energy modulations that create metastable states. Additionally, the indirect effects of the methyl groups on possible base-pair steps neighboring CG:CG are observed to be of comparable importance to their direct effects on CG:CG. The results have implications for the epigenetic control of DNA mechanics.