Traffic congestion is a typical phenomenon when motorways meet urban road networks. At this special location, the weaving area is a recurrent traffic bottleneck. Numerous research activities have been conducted to improve traffic efficiency and sustainability at bottleneck areas. Variable speed limit control (VSL) is one of the effective control strategies. The primary objective of this paper is twofold. On the one hand, turbulent traffic flow is to be smoothed on the special weaving area of motorways and urban roads using VSL control. On the other hand, another control method is provided to tackle the carbon dioxide emission problem over the network. For both control methods, a multi-agent reinforcement learning algorithm is used (MAPPO: multi-agent proximal policy optimization). The VSL control framework utilizes the real-time traffic state and the speed limit value in the last control step as the input of the optimization algorithm. Two reward functions are constructed to guide the algorithm to output the value of the dynamic speed limit enforced within the VSL control area. The effectiveness of the proposed control framework is verified via microscopic traffic simulation using simulation of urban mobility (SUMO). The results show that the proposed control method could shape a more homogeneous traffic flow, and reduces the total waiting time over the network by 15.8%. In the case of the carbon dioxide minimization strategy, the carbon dioxide emission can be reduced by 10.79% in the recurrent bottleneck area caused by the transition from motorways to urban roads.