Spectrum sensing plays a very important role in Cognitive Radio based Internet of Things (CR-IoT) networks for utilization of the licensed spectrum accurately. However, the performance of the conventional Energy Detector (ED) method is compromised in a noise-uncertain environment owing to interference constraints, i.e. the CR-IoT user interference with the licensed Primary User (PU) on the same licensed band. To overcome this drawback, we proposed an energy efficient Cooperative Spectrum Sensing (CSS) for a CR-IoT network with interference constraints using a novel ED method. In this method, each CR-IoT user is capable of spectrum sensing that makes both the local decision and the weight factor based on the sequential approach; we calculate the weight factor against each CR-IoT user based on the Kullback Leibler Divergence award score. After the local decision and the weight factor are made, each CR-IoT user transmits its measured both the local decisions, and the weight factor to a Fusion Center (FC), which is made a final decision about the PU activities based on the hard fusion rule. The simulation results demonstrates that the proposed ED method obtains an improved detection performance, an enhanced sum rate, a spectral efficiency, an energy efficiency, and a lower global error probability when compared to other conventional ED methods under time varying environments.