Wireless powered mobile edge computing has been envisioned as a promising paradigm to enhance the computation capability of low-power wireless devices in Industrial Internet of Things. An efficient resource scheduling method is critical yet challenging to design in such a scenario due to stochastic traffic arrival, time-coupling uplink/downlink decision and incomplete system state knowledge. To tackle these challenges, an online optimization algorithm is proposed in this paper to maximize long-term system utility balancing throughput and fairness, subject to data age and stability constraints. A set of virtual queues is designed to transform the scheduling task, which is hard to solve due to time-dependent data age constraints, into a stochastic optimization problem. Leveraging Lyapunov and convex optimization techniques, the proposed approach can achieve asymptotically near-optimal online decisions without any prior statistical knowledge, and maintain the asymptotic optimality in the presence of partial and outdated network state information. Numerical simulations corroborate the theoretical analysis and demonstrate the effectiveness of the proposed approach.