With the increasing demand for real-time and secure computation in mobile edge computing (MEC) networks, device-enhanced MEC architectures that integrate device-to-device (D2D) communication have emerged as a promising solution. These architectures offload computational tasks by leveraging the processing capabilities of nearby devices, thereby alleviating the burden on edge servers. To enhance secrecy energy efficiency (SEE) while maintaining the timeliness of information processing for tasks, an optimization problem is formulated to maximize the long-term average SEE, subject to latency constraints. Due to the dynamic and heterogeneous inter-user relationships, and the non-convex optimization problem involving mixed discrete and continuous variables, it is challenging to solve using conventional mathematical methods. To tackle these challenges, a graph convolutional twin delayed deep deterministic policy gradient-based resource allocation (GCTD3-RA) method is proposed, where the graph convolutional network (GCN) is used to extract correlation information between users. Extensive simulation results show that the proposed GCTD3-RA method achieves much better SEE than several baselines under different environmental parameters.