Green plastic cover (GPC) is a kind of green plastic fine mesh primarily used for covering construction sites and mitigating large amounts of dust during construction. Accurate GPC detection is vital for monitoring urban environment and understanding urban development. Convolutional neural network (CNN)-based segmentation methods are widely used for detecting object extents, while they rely on high-quality pixel-level labels with high acquisition cost. In this regard, weakly supervised learning can achieve pixel-level segmentation using only image-level labels, by first generating the class activation map (CAM) to obtain initial pixel-level labels and then applying the CNN-based segmentation methods to detect object extents. However, these initial labels are usually incomplete and noisy, caused by the local high response property of CAM. Moreover, the CNN-based segmentation methods often lead to blurry object boundaries due to the gradual down-sampling of feature maps, and meanwhile suffer from the class imbalance problem in real scenarios. Given these problems, we introduce weakly supervised learning into GPC detection to lower the label acquisition cost. Furthermore, to improve the completeness and correctness of initial labels and mitigate the blurry boundary problem, we propose a coarse-to-fine weakly supervised segmentation method (called CFWS), consisting of three steps: 1) object-based label extraction; 2) noisy label correction; and 3) boundary-aware semantic segmentation. Moreover, to alleviate the class imbalance problem, we propose a classification-then-segmentation strategy and integrate it into the CFWS to detect GPC. We test the CFWS on two datasets from Google Earth and Gaofen-2 high-resolution images, respectively. The results show that the CFWS obtains more complete GPCs and effectively retains boundaries on both datasets compared to existing state-of-the-art methods. In real scenarios, the classification-then-segmentation strategy significantly reduces a large number of false alarms generated by direct segmentation. These findings confirm that the CFWS holds great potentials for large-scale GPC detection and urban environmental monitoring. The source code will be available at https://github.com/lauraset/Coarse-to-fine-weakly-supervised-GPC-segmentation.