High-resolution transmission electron microscopy studies show the dynamics of small graphene platelets on larger graphene layers. The platelets move nearly freely to eventually lock in at well-defined positions close to the edges of the larger underlying graphene sheet. While such movement is driven by a shallow potential energy surface described by an interplane interaction, the lock-in position occurs via edge-edge interactions of the platelet and the graphene surface located underneath. Here, we quantitatively study this behavior using van der Waals density functional calculations. Local interactions at the open edges are found to dictate stacking configurations that are different from Bernal (AB) stacking. These stacking configurations are known to be otherwise absent in edge-free two-dimensional graphene. The results explain the experimentally observed platelet dynamics and provide a detailed account of the new electronic properties of these combined systems.