The state prediction of key components in manufacturing systems tends to be risk-sensitive tasks, where prediction accuracy and stability are the two key indicators. The physics-informed neural networks (PINNs), which integrate the advantages of both data-driven models and physics models, are deemed as an effective approach and research trends for stable prediction; however, the potential advantages of PINN are limited for the situations with inaccurate physics models or noisy data, where the balancing of the weights of the data-driven model and physics model is very important for improving the performance of PINN, and it is also a challenge urgently to be addressed. This article proposed a kind of PINN with weighted losses (PNNN-WLs) by uncertainty evaluation for accurate and stable prediction of manufacturing systems, where a novel weight allocation strategy based on uncertainty evaluation by quantifying the variance of prediction errors is proposed, and an improved PINN framework is established for accurate and stable prediction. The proposed approach is verified with open datasets on tool wear prediction, and experimental results show that the prediction accuracy and stability could be obviously improved over existing methods.