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Considering the elasticity of the real networks, the components in the network have a redundant capacity against the load, such as power grids, traffic networks and so on. Moreover, the interaction strength between nodes is often different. This paper proposes a novel nonlinear model of cascade failure in weighted complex networks considering overloaded edges to describe the redundant capacity for edges and capture the interaction strength of nodes. We fill this gap by studying a nonlinear weighted model of cascade failure with overloaded edges over synthetic and real weighted networks. The cascading failure model is constructed for the first time according to the overload coefficient, capacity parameter, weight coefficient, and distribution coefficient. Then through theoretical analysis, the conditions for stopping failure cascades are obtained, and the analysis shows the superiority of the constructed model. Finally, the cascading invulnerability is simulated in several typical network models and the US power grid. The results show that the model is a feasible and reasonable change of weight parameters, capacity coefficient, distribution coefficient, and overload coefficient can significantly improve the destructiveness of complex networks against cascade failure. Our methodology provides an efficacious reference for the control and prevention of cascading failures in many real networks.