Edge computing is an emerging solution to support the future Internet of Things (IoT) applications that are delay-sensitive, processing-intensive or that require closer intelligence. Machine intelligence and data-driven approaches are envisioned to build future Edge-IoT systems that satisfy IoT devices demands for edge resources. However, significant challenges and technical barriers exist which complicate the resource management for such Edge-IoT systems. IoT devices running various applications can demonstrate a wide range of behaviors in the devices resource demand that are extremely difficult to manage. In addition, the management of multidimensional resources fairly and efficiently by the edge in such a setting is a challenging task. In this paper, we develop a novel data-driven resource management framework named BEHAVE that intelligently and fairly allocates edge resources to heterogeneous IoT devices with consideration of their behavior of resource demand (BRD). BEHAVE aims to holistically address the management technical barriers by: 1) building an efficient scheme for modeling and assessment of the BRD of IoT devices based on their resource requests and resource usage; 2) expanding a new Rational, Fair, and Truthful Resource Allocation (RFTA) model that binds the devices BRD and resource allocation to achieve fair allocation and encourage truthfulness in resource demand; and 3) developing an enhanced deep reinforcement learning (EDRL) scheme to achieve the RFTA goals. The evaluation results demonstrate BEHAVEs capability to analyze the IoT devices BRD and adjust its resource management policy accordingly.