Accurate body-weight measurement is important for precision pig farming, but conventional weighing methods are labor-intensive and may disturb normal animal activity. Although three-dimensional sensing systems can provide reliable geometric information, their deployment cost limits large-scale application in commercial farms. This study proposes a non-contact pig weight estimation framework based on standard RGB images. The framework combines SAM 2 foreground extraction with a transformer-based dorsal segmentation network to obtain stable body contours under complex farm conditions. Cross-covariance attention and local patch interaction modules are introduced to preserve both global body structure and local boundary details during segmentation. A hybrid loss function combining focal loss and label-distribution-aware margin loss is further adopted to address foreground-background imbalance. After segmentation, 17 morphometric features are extracted from the dorsal region and used for weight prediction with XGBoost regression. Experiments were conducted on the public PIGRGB-Weight dataset containing 12,476 RGB images from 124 pigs. The proposed method achieved a mean absolute error of 2.983 kg and an $R^2$ value of 0.9891. Compared with a DeepLabV3+-based baseline under the same regression protocol, the proposed framework reduced the prediction error by 24.1%. The results indicate that improving dorsal segmentation quality can substantially enhance the stability of morphometric feature extraction from low-cost RGB images.