Reliable estimation of the State of Health (SOH) in lithium-ion batteries is critical to battery system security and dependability. However, existing Physics-Informed Neural Networks (PINNs) have drawbacks like single-feature physical constraints, rigid fixed-weight fusion of multi-feature constraints and insufficient time-series degradation modeling. To solve these problems, this study proposes an Adaptive-Weight PINN (AW-PINN) optimized by the Grey Wolf Optimizer (GWO) algorithm, which features a dual-LSTM parallel structure and takes incremental capacity peaks and charged capacity as dual physical constraints. A weight generator LSTM adaptively learns weights for monotonicity losses without manual intervention, and GWO globally optimizes physical loss weights to balance data fitting accuracy and prediction physical consistency. Validated on ${\mathrm{LiCoO}}_2$, NCA, and NCM batteries from CALCE and Tongji University datasets via comparative, ablation, and small-sample experiments, AW-PINN shows superior predictive performance (average RMSE = 0.0076; MAE = 0.0065; MAPE = 0.0072), robustness, and generalization. It integrates battery degradation physics with deep learning, retaining strong fitting capability while enabling physical interpretability.