Geiger-mode avalanche photodiode (GM-APD) is a single-photon-detection device characterized by high sensitivity and fast response, which enables it to detect echo signals of distant targets effectively. Given that weak and small targets possess relatively small volumes and occupy only a small number of pixels, relying solely on neighborhood information for target reconstruction proves to be difficult. Furthermore, during long-distance detection, the optical reflection cross-section is small, making signal photons highly susceptible to being submerged by noise. In this paper, a noise fitting and removal algorithm (NFRA) is proposed. This algorithm can detect the position of the echo signal from the photon statistical histogram submerged by noise and facilitate the reconstruction of weak and small targets. To evaluate the NFRA method, this paper establishes an optical detection system for remotely detecting active single-photon weak and small targets based on GM-APD. Taking unmanned aerial vehicles (UAVs) as weak and small targets for detection, this paper compares the target reconstruction effects of the peak-value method and the neighborhood method. It is thereby verified that under the conditions of a 7 km distance and a signal-to-background ratio (SBR) of 0.0044, the NFRA method can effectively detect the weak echo signal of the UAV.