Flow level analysis of communication networks with multiple shared resources is generally difficult. A recently introduced sharing scheme called balanced fairness has brought these systems within the realm of tractability. While straightforward in principle, the numerical evaluation of practically interesting performance metrics like per-flow throughput is feasible for limited state spaces only, besides some specific networks where the results are explicit. In the present paper , we study the behaviour of balanced fairness in light and heavy traffic regimes and show how the corresponding performance results can be used to approximate the flow throughput over the whole load range. The results apply to any network, with a state space of arbitrary dimension. A few examples are explicitly worked out to illustrate the concepts.