The integration of the Industrial Internet of Things (IIoT) and federated learning (FL) can be a promising approach to achieving secure and collaborative AI-driven Industry 4.0 and beyond. FL enables the collaborative training of a global model under the supervision of a central server while ensuring that data remain localized to ensure data privacy. Subsequently, the locally trained models can be aggregated to enhance the global model training process. Nevertheless, the merging of these local models can significantly impact the efficacy of global training due to the diversity of each industry's data. In order to enhance robustness, we propose a Shapley value-based adaptive weighting mechanism that trains the global model as a sequence of cooperative games. The client weights are adjusted based on their Shapley contributions as well as the size and variability of their local datasets in order to improve the model performance. Furthermore, we propose a quantization strategy to mitigate the computational expense of Shapley value computation. Our experiments demonstrate that our method achieves the highest accuracy compared to existing methods due to the efficient assignment of weights. Additionally, our method achieves nearly the same accuracy with significantly lower computational cost by reducing the computation overhead of Shapley value computation in each round of training.