Stochastic resonance (SR), as a type of noise-assisted signal processing method, has been widely applied in weak signal detection and mechanical weak fault diagnosis. In order to further improve the weak signal detection performance of SR-based approaches and realize high-performance weak fault diagnosis, a global parameter optimization (GPO) model of a cascaded SR system is proposed in this work. The cascaded SR systems, which involve multiple multi-parameter-adjusting SR systems with both bistable and tri-stable potential functions, are first introduced. The fixed-parameter optimization (FPO) model and the GPO models of the cascaded systems to achieve optimal SR outputs are proposed based on the particle swarm optimization (PSO) algorithm. Simulated results show that the GPO model is capable of achieving a better SR output compared to the FPO model with rather good robustness and stability in detecting low signal-to-noise ratio (SNR) weak signals, and the tri-stable cascaded SR system has a better weak signal detection performance compared to the bistable cascaded SR system. Furthermore, the weak fault diagnosis approach based on the GPO model of the tri-stable cascaded system is proposed, and two rolling bearing weak fault diagnosis experiments are performed, thus verifying the effectiveness of the proposed approach in high-performance adaptive weak fault diagnosis.