Vertical stacking of monolayers via van der Waals (vdW) assembly is an emerging field that opens promising routes toward engineering physical properties of two-dimensional materials. Industrial exploitation of these engineering heterostructures as robust functional materials still requires bounding their measured properties so as to enhance theoretical tractability and assist in experimental designs. Specifically, the short-range attractive vdW forces are responsible for the adhesion of chemically inert components and are recognized to play a dominant role in the functionality of these structures. Here, we reliably quantify the strength of ambient vdW forces in terms of an effective Hamaker coefficient for chemical vapor deposition grown graphene and show how it scales by a factor of two or three from single to multiple layers on standard supporting surfaces such as copper or silicon oxide. Furthermore, direct measurements on freestanding graphene provide the means to discern the interplay between the vdW potential of graphene and its supporting substrate. Our results demonstrated that the underlying substrates could be controllably exploited to enhance or reduce the vdW force of graphene surfaces. We interpret the physical phenomena in terms of a Lifshitz theory-based analytical model.