Weighted sum rate maximization (WSRM) for precoder optimization effectively balances performance and fairness among users. Recent studies have demonstrated the potential of deep learning in precoder optimization for sum rate maximization. However, the WSRM problem necessitates a redesign of neural network architectures to incorporate user weights into the input. In this paper, we propose a novel deep neural network (DNN) to learn the precoder for WSRM. Compared to existing DNNs, the proposed DNN leverage the joint unitary and permutation equivariant property inherent in the optimal precoding policy, effectively enhancing learning performance while reducing training complexity. Simulation results demonstrate that the proposed method significantly outperforms baseline learning methods in terms of both learning and generalization performance while maintaining low training and inference complexity.