The accurate estimation of fish weight relies on the crucial parameter of individual fish contour features. While instance segmentation proves effective in extracting fish contours, challenges arise from diverse fish postures and reduced image sharpness underwater. Current instance segmentation methods often struggle to effectively balance global and local detailed features, which can result in inaccurate positioning of contour keypoints and consequently limit the accuracy of fish weight estimation. To overcome this, our study introduces a novel instance segmentation network tailored for precise fish contour extraction. The proposed approach incorporates multi-scale feature fusion and an attention mechanism based on the Segmenting Objects by Locations (SOLO) network, referred to as SOLO-MFFA. This paper designs a multi-scale context aggregation module to integrate features with a wider range of receptive fields, augmenting the model's capability to comprehend both local features and global information. At the same time, the introduction of a mixed-domain attention mechanism emphasizes more critical channel features and simultaneously improves the localization accuracy of contour points. Compared with SOLO and its improved model CAM-SOLO on the fish instance segmentation dataset, SOLO-MFFA demonstrated an effective improvement, with a 4.3% and 1.6% increase in mAP (mean Average Precision), respectively. The Decoupled-SOLO-MFFA achieved higher mAP. The visualization results also demonstrate that the contour features extracted in this paper are smoother and more accurately positioned. Additionally, in comparison to other well-known instance segmentation networks, our method has demonstrated significant improvements in both qualitative and quantitative evaluations. Furthermore, the integration of contour features derived from Decoupled-SOLO-MFFA, along with binocular vision, was utilized for the precise estimation of fish perimeter and weight. The findings reveal a strong correlation between the perimeter calculated by Decoupled-SOLO-MFFA and the actual weight, with a notably reduced error in weight estimation. Compared to previous methods, RMSE, MAE, and MAPE of the linear model constructed in this paper decreased by 3.92, 3.19, and 1.4%.