Cyber-Physical Systems (CPS) consist of various physical devices and have a significant impact on both industry and the economy. In CPS, controllers or control centers typically send continuous commands to actuators. Due to the limited computational and storage resources of CPS devices, existing Message Authentication Code and digital signature algorithms face challenges in terms of being non-interactive, lightweight, and continuous on the actuator side. To address this issue, we propose a lightweight continuous message authentication (LCMA) scheme that ensures the continuity of signatures through a mechanism involving random numbers and incrementing sub-private keys. The multidimensional Bloom filters is designed and used togather with precomputed verification points generated by Key Generation Center to enable non-interactive verification. Additionally, we design a redundancy-free hash tree for CPS to reduce information redundancy. The proposed solution requires only hash operations and Bloom filter queries for verification, achieving sufficient lightweight performance. Finally, we provide a formal security proof for the proposed scheme and simulate it on the ESP32 platform. The results show that the implementation times for signature generation and verification are 0.779 milliseconds and 0.792 milliseconds, respectively. Compared to other non-interactive lightweight message authentication schemes, the proposed LCMA is more suitable for CPS devices.