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With the formation of urban agglomerations, economic zones, and metropolitan areas, the supporting role of the regional logistics industry in economic development is becoming increasingly prominent. It is of great significance to study the spatiotemporal evolution and the coordinated development of regional logistics networks to realize regional integration. In this paper, we propose the weighted co-evolution model of regional logistics networks based on node attraction by introducing concepts such as logistics attractiveness, geographic space distance, and logistics node level, and we integrate the true regional situation into the evolution model. Taking the Chengdu–Chongqing region as an example, we analyze the co-evolution simulation of the area’s regional logistics network. The results show that (1) there are three node connections between new and original nodes, and 50 nodes are added per time interval, which is an ideal situation for studying the evolution of a regional logistics network; (2) the future evolution of the regional logistics network in the Chengdu–Chongqing region can be divided into three stages: the initial construction period from the initial state to the T2 stage, the slow maturity period from T2 to T3, and the coordinated development period from T3 to T4. This research serves as a reference for government managers to formulate logistics development plans.