Densities and osmotic coefficient measurements for dilute aqueous solutions of glycine, L-leucine, and glycylglycine have been reported at 298.15 K. The partial molar volumes and activity coefficients of solute as well as solvent have been estimated using the density and osmotic coefficient data, respectively. Excess and mixing thermodynamic properties, such as Gibbs free energy, enthalpy, and entropy changes, have been obtained using the activity data from this study and the heat data reported in the literature. The concentration enthalpy-entropy compensation effects have been observed for the studied systems, and the compensation temperatures are reported. It has been observed that the excess free energy change for all the studied systems is almost the same over the studied concentration range, showing that the differences in properties of such solutions are largely decided by the enthalpy-entropy effects. These results, along with partial entropy data, show the effects of the presence of hydrophobic interactions and water structure making effect in the case of aqueous solutions of L-leucine. The application of the Starikov-Norden enthalpy-entropy compensation model yielded information about a "hidden Carnot cycle" and the existence of multiple microphases. Application of the Kirkwood-Buff (KB) theory of solutions for the studied systems yields pair correlation functions between the components. The variation of Kirkwood-Buff integrals with concentration further signifies the concentration dependence of the hydrophobic hydration and interactions in the solution phase. The osmotic second virial coefficients have also been obtained using the KB theory and show good agreement with those obtained using the McMillan-Mayer theory of solutions. The mean square concentration fluctuations is estimated using the KB theory, which gives information about the microheterogeneity in the solution phase, which further reflects the presence of hydration and solute association.