Unmanned Aerial Vehicle (UAV)-assisted Mobile Edge Computing (MEC) can provide mobile users (MU) with additional computing services and a wide range of connectivity. This paper investigates the joint optimization strategy of task offloading and resource allocation for UAV-assisted MEC systems in complex scenarios with the goal of reducing the total system cost, consisting of task execution latency and energy consumption. We adopt a game theoretic approach to model the interaction process between the MEC server and the MU Stackelberg bilayer game model. Then, the original problem with complex multi-constraints is transformed into a duality problem using the Lagrangian duality method. Furthermore, we prove that the modeled Stackelberg bilayer game has a unique Nash equilibrium solution. In order to obtain an approximate optimal solution to the proposed problem, we propose a two-stage alternating iteration (TASR) algorithm based on the subgradient method and the marginal revenue optimization method. We evaluate the effective performance of the proposed algorithm through detailed simulation experiments. The simulation results show that the proposed algorithm is superior and robust compared to other benchmark methods and can effectively reduce the task execution latency and total system cost in different scenarios.