Wireless body area networks (WBANs) consist of a number of low-power sensors, through which specialists can remotely monitor the real-time vital parameters of patients. This facility can improve healthcare quality and reduce associated costs considerably. However, WBAN devices typically have limited resources that severely hinder the quality of services. To alleviate these limitations, the concept of cloud-assisted WBANs has been proposed. In such networks, the cloud server provides extensive computational and storage resources for processing and storing the collected data. However, outsourcing data to a third-party provider raises concerns over data confidentiality, data integrity, and fine-grained access and search control. To address these concerns, we put forward a Lightweight Verifiable Data Management (LVDM) scheme. Our scheme offers efficient fine-grained access and search control mechanisms. Also, in LVDM, the computational overhead incurred by sensors is very low, and almost all computational tasks in the data encryption, data retrieval, and decryption phases are performed by the cloud server. Moreover, our scheme enables users to remotely check the data integrity and the accuracy of operations performed by the cloud. Our detailed security and performance analysis demonstrates that LVDM is provable secure and yields better performance over other similar schemes.