Clouds significantly affect the quality of optical satellite images, which seriously limits their precise application. Recently, deep learning has been widely applied to cloud detection and has achieved satisfactory results. However, the lack of distinctive features in thin clouds and the low quality of training samples limit the cloud detection accuracy of deep learning methods, leaving space for further improvements. In this paper, we propose a weakly supervised cloud detection method that combines spectral features and multi-scale scene-level deep network (SpecMCD) to obtain highly accurate pixel-level cloud masks. The method first utilizes a progressive training framework with a multi-scale scene-level dataset to train the multi-scale scene-level cloud detection network. Pixel-level cloud probability maps are then obtained by combining the multi-scale probability maps and cloud thickness map based on the characteristics of clouds in dense cloud coverage and large cloud-area coverage images. Finally, adaptive thresholds are generated based on the differentiated regions of the scene-level cloud masks at different scales and combined with distance-weighted optimization to obtain binary cloud masks. Two datasets, WDCD and GF1MS-WHU, comprising a total of 60 Gaofen-1 multispectral (GF1-MS) images, were used to verify the effectiveness of the proposed method. Compared to the other weakly supervised cloud detection methods such as WDCD and WSFNet, the F1-score of the proposed SpecMCD method shows an improvement of over 7.82%, highlighting the superiority and potential of the SpecMCD method for cloud detection under different cloud coverage conditions.