To enhance the precision and robustness of constrained evolutionary algorithms for handling various constrained many-objective problems, this paper proposes a constrained many-objective evolutionary algorithm based on adaptive two-stage hierarchical equilibrium. The algorithm combines a multi-stage optimization approach with hybrid constraint handling techniques. Firstly, it designs segmentation timing based on dynamic individual dominance relationships and adaptively switches between the objective function-focused phase and the constraint handling-focused phase. Then, it constructs a hybrid hierarchical equilibrium criterion based on population evolution information, employing an adaptive random ranking method to select individuals in infeasible situations and defining a semi-feasibility criterion for selecting individuals in semi-feasible situations. This approach maintains a dynamic balance between feasible and infeasible solutions, improving population convergence, distribution, and diversity. Extensive experiments on standard test function sets C_DTLZ, DC_DTLZ, and MW show that the proposed algorithm achieves better convergence performance and stability across different objective dimensions and various constrained high-dimensional multi-objective problems with narrow, discrete, or disconnected feasible regions, and demonstrates that the proposed algorithm has higher convergence accuracy and better robustness compared to five advanced methods, namely MOEA/D-FCHT, MOEA/D-2WA, PPS, ToP, and Trip.