In order to discuss the robustness of weighted complex networks against cascading failures, this paper proposes a betweenness-dependent node weighting method, and constructs a cascading model with tunable weight parameters by applying the local weighted flow redistribution rule. Cascading behaviors on both model and real-world networks are studied. The numerical simulation and theoretical analysis results give a value of the weight parameter corresponding to the strongest robustness level for the networks. The betweenness-dependent weighting strategy makes the...