Distributed processing is becoming more important in robotics as low-cost ad hoc networks provide a scalable and robust alternative to tradition centralized processing. Gaussian belief propagation (GaBP) is an effective message-passing algorithm for performing inference on distributed networks, however, its accuracy and convergence can be significantly decreased as networks have higher connectivity and loops. This paper presents two empirically derived methods for weighting the messages in GaBP to minimize error. The first method uses uniform weights based on the average node degree across the network, and the second uses weights determined by the degrees of the nodes at either end of an edge. Extensive simulations show that this results in greatly decreased error, with even greater effects as the network scales. Finally, we present a practical application of this algorithm in the form of a multi-robot localization problem, with our weighting system improving the accuracy of the solution.