To address inefficiency and subjectivity of manual eaves tile dating methods， a Hypergraph-based Eaves Tile Dating method under Data Imbalance Conditions （HETD-DIC） was proposed to provide a more objective assistive tool for archaeological dating. Firstly， a dual-weight computation mechanism was designed， which means that a hyperedge weight computation module was used to aggregate associated node features， so as to generate hyperedge weights， and these hyperedge weights were then used to calculate node weights， which reduced the impact of imbalanced sample distribution. Secondly， a Hyperedge Node Relation Matrix （HNRM） was constructed to establish a feature encoding-decoding channel， so as to enhance the representation capability of nodes. Finally， extensive experiments were conducted to evaluate different models， and UniGIN （Unified Graph Isomorphism Network） was selected as baseline classification model due to its superior performance. Experimental results demonstrate that on the self-built eaves tile dataset， with only 20% of training data used， HETD-DIC achieves improvements of 4.67， 4.55， 4.67， and 5.09 percentage points， respectively， compared to UniGIN in accuracy， weighted precision， weighted recall， and weighted F1-score. It can be seen that HETD-DIC solves data imbalance problem effectively and provides reliable automatic assisted decision basis for archaeological dating.