Reducing traffic energy consumption is crucial for smart cities, and vehicle carbon emissions are a key energy indicator. Traffic signal control (TSC) is a useful method because it can affect the energy consumption of vehicles on the road by controlling the stop-and-go of vehicles at traffic intersections. However, setting traffic signals to reduce energy consumption will affect traffic efficiency and this is not in line with traffic management objectives. Current studies adopt multi-objective optimization methods with high traffic efficiency and low carbon emissions to solve this problem. However, most methods use static weights, which cannot adapt to complex and dynamic traffic states, resulting in non-optimal performance. Current energy indicators for urban transportation often fail to consider passenger fairness. This fairness is significant because the purpose of urban transportation is to serve people’s mobility needs not vehicles. Therefore, this paper proposes Multi-objective Adaptive Meta-DQN TSC (MMD-TSC), which introduces a dynamic weight adaptation mechanism to simultaneously optimize traffic efficiency and energy saving, and incorporates the per capita carbon emissions as the energy indicator. Firstly, this paper integrates traffic state data such as vehicle positions, velocities, vehicle types, and the number of passengers and incorporates fairness into the energy indicators, using per capita carbon emissions as the target for reducing energy consumption. Then, it proposes MMD-TSC with dynamic weights between energy consumption and traffic efficiency as reward functions. The MMD-TSC model includes two agents, the TSC agent and the weight agent, which are responsible for traffic signal adjustment and weight calculation, respectively. The weights are calculated by a function of traffic states. Finally, the paper describes the design of the MMD-TSC model learning algorithm and uses a SUMO (Simulation of Urban Mobility) v.1.20.0 for traffic simulation. The results show that in non-highly congested traffic states, the MMD-TSC model has higher traffic efficiency and lower energy consumption compared to static multi-objective TSC models and single-objective TSC models, and can adaptively achieve traffic management objectives. Compared with using vehicle average carbon emissions as the energy consumption indicator, using per capita carbon emissions achieves Pareto improvements in traffic efficiency and energy consumption indicators. The energy utilization efficiency of the MMD-TSC model is improved by 35% compared to the fixed-time TSC.