The Industrial Internet of Things (IIoT) leverages Federated Learning (FL) for distributed model training while preserving data privacy, and meta-computing enhances FL by optimizing and integrating distributed computing resources, improving efficiency and scalability. Efficient IIoT operations require a trade-off between model quality and training latency. Consequently, a primary challenge of FL in IIoT is to optimize overall system performance by balancing model quality and training latency. This paper designs a satisfaction function that accounts for data size, Age of Information (AoI), and training latency for meta-computing. Additionally, the satisfaction function is incorporated into the utility function to incentivize IIoT nodes to participate in model training. We model the utility functions of servers and nodes as a two-stage Stackelberg game and employ a deep reinforcement learning approach to learn the Stackelberg equilibrium. This approach ensures balanced rewards and enhances the applicability of the incentive scheme for IIoT. Simulation results demonstrate that, under the same budget constraints, the proposed incentive scheme improves utility by at least 23.7% compared to existing FL schemes without compromising model accuracy.