This paper presents a support for the development of Distributed Virtual Environments (DVEs) on P2P architectures. A hierarchical overlay is defined by pairing each peer with a weight which is proportional to its networking bandwidth. Peers characterized by higher weights are assigned a greater workload, in terms of connections with other peers and of number of passive objects they manage, and can act as superpeers that offer a set of services to peers characterized by lower bandwidth. Additively Weighted Voronoi (AWV) Diagrams are exploited to define a partition of the DVE that assigns to each peer a region whose size is dependent on the peer's weight. Superpeers are modeled by sites of the tessellation that have absorbed at least the Voronoi region of another site. A set of experimental results shows that this approach can be a load balancing mechanism for peer-to-peer networks, that does not impair usual properties of Voronoi-based peer-to-peer networks.