We apply both integral equation and Monte Carlo (MC) simulation methods to investigate effects of solute size on local solvent clustering about the solute and on the solute residual chemical potential change in infinitely dilute supercritical solutions. We find that monitoring the net local solvent density changes within the first solvation shell offers a predictive way, complementary to the residual solute chemical potential calculations, to study the trend of solubility change in dilute supercritical solutions. The integral equation calculations indicate that a large solute (if it has the same energy parameter as the solvent molecule) tends to reduce its local density when the bulk solvent density is high. MC simulations support the integral equation results. This result is also consistent with the solute-solvent size-ratio dependence of residue chemical potentials from the test particle MC simulation.