Internet of Things (IoT) is a network of physical objects or things that can communicate and share information. In IoT-enabled Wireless Medical Sensor Network (WMSN), the smart sensing devices share remote patient monitoring data towards central repositories. During medical data aggregation and transmission, security is mandatory to guard against intruders. The main problem in existing base schemes is that complex multiplication operations are used for batch key creation. These schemes are computationally expensive and require huge memory space at the aggregator node (AN). This paper presents a lightweight Secure Aggregation and Transmission Scheme (SATS) for secure and lightweight data computation and transmission. SATS provides a lightweight XOR operation for obtaining batch keys instead of the expensive multiplication operation. Furthermore, the AN Receiving Message Algorithm (ARMA) is presented at the AN to aggregate data generated by sensor nodes. The Receiving Message Extractor (RME) algorithm is presented to decrypt the message and perform batch verification at the Fog-Server. SATS protects against several security threats such as denial of service attacks, the man in the middle attack, and reply attacks. The proposed SATS is simulated by using simulation tool NS 2.35. The results show that SATS provides lightweight data transmission by reducing computation and communication costs.The computation cost of the SATS scheme is 14%, 23% and 59% at AN, and at Fog-Node 6.5%, 21.5% and 51%, and Communication cost 6%, 3%, and 4% at Sensor Node, and at AN 6%, 9%, and 12% better than PPDAS, IDAP, and ASAS respectively. The proposed SATS is compared with relevant schemes and the results show that it provides better storage capacity, computations cost, communications cost, and energy consumption.