Accurately recognizing and assessing pain in sheep is key to discern animal health and mitigating harmful situations. However, such accuracy is limited by the ability to manage automatic monitoring of pain in those animals. Facial expression scoring is a widely used and useful method to evaluate pain in both humans and other living beings. Researchers also analyzed the facial expressions of sheep to assess their health state and concluded that facial landmark detection and pain level prediction are essential. For this purpose, we propose a novel weighted graph neural network (WGNN) model to link sheep's detected facial landmarks and define pain levels. Furthermore, we propose a new sheep facial landmarks dataset that adheres to the parameters of the Sheep Facial Expression Scale (SPFES). Currently, there is no comprehensive performance benchmark that specifically evaluates the use of graph neural networks (GNNs) on sheep facial landmark data to detect and measure pain levels. The YOLOv8n detector architecture achieves a mean average precision (mAP) of 59.30% with the sheep facial landmarks dataset, among seven other detection models. The WGNN framework has an accuracy of 92.71% for tracking multiple facial parts expressions with the YOLOv8n lightweight on-board device deployment-capable model.