The multi-view clustering methods based on tensor regression can make full use of the potential structural information between views and achieve data-level fusion. However, existing tensor regression-based approaches for anchor graph often overlook the probabilistic nature of anchor graph, focusing solely on sample labels while ignoring the influence of anchor labels on clustering results. To overcome these limitations, we introduce Tensorized Label Learning via Balanced Tensor Regression (TLL-BTR). Our key idea is to exploit the probabilistic nature of the anchor graph by regarding the sample labels as a projection tensor that maps the anchor graph into the label space, thereby producing anchor labels. By enforcing constraints on these anchor labels, we guide the concurrent learning of sample labels and achieve co-label learning between anchors and samples. To prevent trivial solutions, we maximize the nuclear norm to promote an even distribution of samples across clusters. Extensive experiments on benchmark datasets demonstrate that TLL-BTR consistently outperforms state-of-the-art methods.