Segmenting dark-field images of laser-induced damage on large-aperture optics in high-power laser facilities is challenged by complicated damage morphology, uneven illumination and stray light interference. Fully supervised semantic segmentation algorithms have achieved state-of-the-art performance but rely on a large number of pixel-level labels, which are time-consuming and labor-consuming to produce. LayerCAM, an advanced weakly supervised semantic segmentation algorithm, can generate pixel-accurate results using only image-level labels, but its scattered and partially underactivated class activation regions degrade segmentation performance. In this paper, we propose a weakly supervised semantic segmentation method, continuous gradient class activation mapping (CAM) and its nonlinear multiscale fusion (continuous gradient fusion CAM). The method redesigns backpropagating gradients and nonlinearly activates multiscale fused heatmaps to generate more fine-grained class activation maps with an appropriate activation degree for different damage site sizes. Experiments on our dataset show that the proposed method can achieve segmentation performance comparable to that of fully supervised algorithms.