The characteristic properties of graphene make it useful in an assortment of applications. One particular application--the use of graphene in biosensors--requires a thorough understanding of graphene-peptide interactions. In this study, the binding of glycine (G) capped amino acid residues (termed GXG tripeptides) to trilayer graphene surfaces in aqueous solution was examined and compared to results previously obtained for peptide binding to single-layer free-standing graphene [A. N. Camden, S. A. Barr, and R. J. Berry, J. Phys. Chem. B 117, 10691-10697 (2013)]. In order to understand the interactions between the peptides and the surface, binding enthalpy and free energy values were calculated for each GXG system, where X cycled through the typical 20 amino acids. When the GXG tripeptides were bound to the surface, distinct conformations were observed, each with a different binding enthalpy. Analysis of the binding energy showed the binding of peptides to trilayer graphene was dominated by van der Waals interactions, unlike the free-standing graphene systems, where the binding was predominantly electrostatic in nature. These results demonstrate the utility of computational materials science in the mechanistic explanation of surface-biomolecule interactions which could be applied to a wide range of systems.