Objective. The goal of this study is to develop a robust semi-weakly supervised learning strategy for vessel segmentation in laser speckle contrast imaging (LSCI), addressing the challenges associated with the low signal-to-noise ratio, small vessel size, and irregular vascular aberration in diseased regions, while improving the performance and robustness of the segmentation method. Approach. For the training dataset, the healthy vascular images denoted as normal-vessel samples were manually labeled, while the diseased LSCI images involving tumor or embolism were denoted as abnormal-vessel samples and annotated as pseudo labels by the traditional semantic segmentation methods. In the training phase, the pseudo labels were constantly updated to improve the segmentation accuracy based on DeepLabv3+. Objective evaluation was conducted on the normal-vessel test set, while subjective evaluation was performed on the abnormal-vessel test set. Main results. The proposed method achieved an IOU of 0.8671, a Dice of 0.9288, and a mean relative percentage difference (mRPD) with supervised learning of 0.5% in the objective evaluation. In the subjective evaluation, our method significantly outperformed other methods in main vessel segmentation, tiny vessel segmentation, and blood vessel connection. Additionally, our method exhibited robustness when abnormal-vessel style noise was added to normal-vessel samples using a style translation network. Significance. The proposed semi-weakly supervised learning strategy demonstrates high efficiency and excellent robustness for vascular segmentation in LSCI, providing a potential tool for assessing the morphological and structural features of vessels in clinical applications.