Wireless Body Area Network (WBAN) is a quite suitable communication tool for medical IoT devices that are deployed to collect physiological parameters and forecast real-time events in order to facilitate the diagnostic decision-making for the medical staff. However, sensor readings may be inaccurate due to resource-constrained devices, sensor misplacement, hardware faults, and other environmental factors. Therefore, anomaly detection is envisioned as a promising approach to deal with unreliable and malicious data injection to improve remote patient monitoring systems and reduce false medical diagnosis. In this context, several data analysis and machine learning tools have been proposed to detect abnormal deviations in WBAN. Nevertheless, no one considers the dynamic context changes of WBAN to provide adaptive and dynamic outlier detection. In addition, most of them ignore the co-existence of strong spatial and temporal correlations between monitored physiological attributes. To this end, we propose a two-level lightweight and adaptive anomaly detection approach to discard false alarms caused by faulty measurements and raise alarms only when a patient seems to be in emergency situations. In the first level, a game-theoretic technique is introduced wherein body-worn sensor nodes exploit the spatiotemporal correlation among readings to locally and adaptively detect anomalous events according to the dynamic context changes of WBAN. In the second level, we apply the Mahalanobis distance in the Local Processing Unit (LPU) which has a global view for multivariate analysis. Our main objective is to ensure a tradeoff between detection accuracy, false positive rates, and network performance while considering the WBAN environment constraints. The proposed approach is evaluated through numerical simulations on a real physiological data set. Simulation results prove the effectiveness of the proposed approach in terms of achieving high detection accuracy with low false alarm rate and energy consumption.