By construction, an eigenvariety comes with a map to the weight space. It is natural to ask what the ramification locus is. For Hilbert eigenvariety, we characterize the classical ramification points in terms of the associated Galois representation. This comes from the classicality theorem due to Tian-Xiao using cohomological methods, and a lower bound on the dimension of the tangent space of the weight fiber using Galois deformation. We would also mention how the ramification behaviors of the classical point and its companion points are related.