Hydration effects on a pair of methane molecules are investigated by extensive constant-pressure (NPT) sampling using the TIP4P model of water under 1, 1000, 2000, and 3000 atm. The volume distributions of pure water and of methanes plus water are determined directly as functions of methane-methane distance e. The corresponding excess isothermal and adiabatic compressibilities are estimated from the pressure-dependent methane excess volume. The dependence of excess volume on xi is oscillatory for small xi. The maxima of excess volume and compressibility are seen near the desolvation barrier (db) of the potential of mean force (PMF). These features may be understood by the development, near the db, of a void volume encased by a molecular (Connolly) surface defined using a water-sized probe. These db properties for two methanes are consistent with well-corroborated experimental observations of positive activation volumes for protein folding and some experiments suggesting a slightly higher compressibility for the folding transition state than the unfolded state. At high pressures, the volumes at the PMF solvent-separated minimum and the contact-minimum configurations are both smaller than the volume at large xi. This trend provides a rationalization for the compactness of pressure-denatured states of proteins. Taking the packing densities of pure nonpolar phases into consideration, our simulation results suggest that whether the activation volume of unfolding is positive or negative hinges on the packing compactness of the protein core. Volume change can be but is not necessarily monotonic along the folding pathway.