Remote monitoring of drones has become a global objective due to emerging applications in national security and managing aerial delivery traffic. Despite their relatively small size, drones can carry significant payloads, which require monitoring, especially in cases of unauthorized transportation of dangerous goods. A drone's flight dynamics heavily depend on outdoor wind conditions and the carry-on weight, which affect the tilt angle of a drone's body and the rotation velocity of the blades. A surveillance radar can capture both effects, provided a sufficient signal-to-noise ratio for the received echoes and an adjusted postprocessing detection algorithm. Here, we conduct a systematic study to demonstrate that micro-Doppler analysis enables the disentanglement of the impacts of wind and weight on a hovering drone. The physics behind the effect is related to the flight controller, as the way the drone counteracts weight and wind differs. When the payload is balanced, it imposes an additional load symmetrically on all four rotors, causing them to rotate faster, thereby generating a blade-related micro-Doppler shift at a higher frequency. However, the impact of the wind is different. The wind attempts to displace the drone, and to counteract this, the drone tilts to the side. As a result, the forward and rear rotors rotate at different velocities to maintain the tilt angle of the drone body relative to the airflow direction. This causes the splitting in the micro-Doppler spectra. By performing a set of experiments in a controlled environment, specifically, an anechoic chamber for electromagnetic isolation and a wind tunnel for imposing deterministic wind conditions, we demonstrate that both wind and payload details can be extracted using a simple deterministic algorithm based on branching in the micro-Doppler spectra.