Managing and balancing load in distributed systems remains a challenging problem in resource management, especially in networked systems where scalability concerns favour distributed and dynamic approaches. Distributed methods can also integrate well with centralised control paradigms if they provide high-level usage statistics and control interfaces for supporting and deploying centralised policy decisions. We present a general method to compute target values for an arbitrary metric on the local system state and show that autonomous rebalancing actions based on the target values can be used to reliably and robustly improve the balance for metrics based on probabilistic risk estimates. To balance the trade-off between balancing efficiency and cost, we introduce 2 methods of deriving rebalancing actuations from the computed targets that depend on parameters that directly affects the trade-off. This enables policy level control of the distributed mechanism based on collected metric statistics from network elements. Evaluation results based on cellular radio access network simulations indicate that load balancing based on probabilistic overload risk metrics provides more robust balancing solutions with fewer handovers compared to a baseline setting based on average load.