Compressive sensing (CS) has been widely used to sense the wideband spectrum with fewer measurements by taking advantage of radio spectrum underutilization. As new smart devices, such as IoT devices, smart home devices, and wearables, use batteries and have limited memory, more research is needed to reduce the overuse of cognitive radio (CR) resources through spectrum sensing. To reduce the number of compressive measurements required for spectrum recovery, researchers proposed approaches like weighted and sequential compressive sensing. In this paper, we estimate the primary user’s (PU) behavior statistics and use the estimated information in a novel weighted sequential compressive spectrum sensing approach. Our proposed approach can reduce and adapt the number of measurements and the sensing time to the changing number of active channels in a dynamically changing wideband spectrum.