Fact verification task has emerged as an essential research topic recently due to abundant fake news spreading on the Internet. The task based on unstructured data (i.e., news) has achieved great development, but the task based on structured data (i.e., table) is still in the primary development period. The existing methods usually construct complete heterogeneous graph networks around statement, table, and program subgraphs, and then infer to learn similar semantics on them for fact verification. However, they generally connect the nodes with the same content between subgraphs directly to frame a larger graph network, which has serious sparsity in connections, especially when subgraphs possess limited semantics. To this end, we propose tight-fitting graph inference network (TFGIN), which innovatively builds tight-fitting graphs (TF-graphs) to strengthen the connections of subgraphs and designs inference modeling layer (IML) to learn coherence evidence for fact verification. Specifically, different from traditional connection ways, the constructed TF-graph enhances inter-graph and intra-graph connections of subgraphs through subgraph segmentation and interaction guidance mechanisms. IML could reason the semantics with strong correlation and high consistency as explainable evidence. Experiments on three competitive datasets confirm the superiority and scalability of our TFGIN.