Topology control in a wireless sensor network is useful for ensuring that the network remains connected in the presence of nodes that exhaust their energy or become altogether dysfunctional (for whatever reasons). It also ensures that all the link that can be established are energy-efficient links and the nodes utilize their energy fairly. In this paper, we propose a fair and energy efficient topology control protocol for a two-dimensional random sensor deployment in which the nodes can estimate the distances to their neighbors and vary their transmission power accordingly. The protocol applies a neighbor eligibility metric in order to ensure a fair distribution of energy in the network. We introduce the notion of weighted relaying regions defined over the plane of a searching node to drop out inefficient links. Unlike most topology control protocols that rely on nearest neighbor approaches, we use a distance measure that is radio characteristic and channel condition dependent. We verify the performance of the protocol through simulation results on network graph properties and energy consumption.