Machine learning has been widely applied in oilfield exploration and development. However, purely data-driven machine learning models face challenges regarding high data dependency and weak generalizability. Furthermore, these models often neglect the domain knowledge behind the data. This paper integrates physical knowledge with machine learning architectures and develops a weight-adaptive residual-enhanced and physics-constrained machine learning (WR-PCML) framework for reservoir pressure prediction in small data regime. First, a physics-constrained machine learning (PCML) architecture for reservoir pressure prediction is proposed to embed laws of physics into the machine learning algorithm. Subsequently, a weight-adaptive adjustment strategy based on multiobjective optimization is proposed to optimize the PCML model parameters by simultaneously considering the gradients of all of the loss terms. Finally, the systematic residuals between the observations and physics are compensated for by a residual enhancement mechanism, and the WR-PCML model is constructed. Compared with benchmark methods such as theory-guided neural networks, WR-PCML mitigates the sensitivity to manual weight setting through the adaptive loss strategy. Additionally, the residual-enhanced module improves the prediction of physics-constrained models with incomplete mechanisms resulting from noise and measurement errors. The experimental results demonstrate that WR-PCML can accurately predict long-term reservoir pressure using short-term small data, outperforming benchmark methods by 40.63% in two-dimensional and 25.81% in three-dimensional pressure prediction scenarios.