The air ground integrated networks can leverage unmanned aerial vehicle (UAV) communications to tackle the ever-increasing and unbalanced traffic load in future communication systems. This paper investigates the UAV enabled traffic offloading problem in air ground integrated networks with mixed user traffic. The problem jointly maximizes the system load balance and the total UAV reward, which can be formulated under a two-layer network graph model. In the cellular network graph, the association between the delay-sensitive users and the access points (APs) as well as the association between the UAVs and the APs are formulated. In the UAV network graph, the association between the delay-insensitive users and the UAVs is formulated. By observing the coupling relationship of the decision variables, we decouple the problem into three sub-problems and solve the first two sub-problems with reduced complexity. Then, we devise a Deep Neural Network (DNN) empowered genetic algorithm to solve the last sub-problem. The DNN can be leveraged to filter out the non-optimal solutions in the initialization operator of the genetic algorithm for improving the efficiency. Performance comparisons are provided between the proposed traffic offloading scheme and the existing ones, which validate the advantages of the DNN empowered genetic algorithm regarding its convergence, accuracy, and robustness.