Instance segmentation in remote sensing (RS) imagery aims to predict the locations of instances and represent them with pixel-level masks. Thanks to the more accurate pixel-level information for each instance, instance segmentation has enormous potential applications in resource planning, urban surveillance, and military reconnaissance. However, current RS imagery instance segmentation methods mostly follow the fully supervised paradigm, relying on expensive pixel-level labels. Moreover, remote sensing imagery suffers from cluttered backgrounds and significant variations in target scales, making segmentation challenging. To accommodate these limitations, we propose a semantic attention enhancement and structured model-guided multi-scale weakly supervised instance segmentation network (SASM-Net). Building upon the modeling of spatial relationships for weakly supervised instance segmentation, we further design the multi-scale feature extraction module (MSFE module), semantic attention enhancement module (SAE module), and structured model guidance module (SMG module) for SASM-Net to enable a balance between label production costs and visual processing. The MSFE module adopts a hierarchical approach similar to the residual structure to establish equivalent feature scales and to adapt to the significant scale variations of instances in RS imagery. The SAE module is a dual-stream structure with semantic information prediction and attention enhancement streams. It can enhance the network’s activation of instances in the images and reduce cluttered backgrounds’ interference. The SMG module can assist the SAE module in the training process to construct supervision with edge information, which can implicitly lead the model to a representation with structured inductive bias, reducing the impact of the low sensitivity of the model to edge information caused by the lack of fine-grained pixel-level labeling. Experimental results indicate that the proposed SASM-Net is adaptable to optical and synthetic aperture radar (SAR) RS imagery instance segmentation tasks. It accurately predicts instance masks without relying on pixel-level labels, surpassing the segmentation accuracy of all weakly supervised methods. It also shows competitiveness when compared to hybrid and fully supervised paradigms. This research provides a low-cost, high-quality solution for the instance segmentation task in optical and SAR RS imagery.