Existing deep graph clustering methods are limited by their reliance on static initial graph structures, which are often incomplete or biased and fail to capture the dynamic changes in node similarities. To address these issues, an adaptive weighted deep graph clustering based on a graph attention autoencoder (AWDGC) is proposed. First, a trainable generalized Mahalanobis distance combined with a Gaussian kernel function is introduced to adaptively assign edge weights for constructing a weighted adjacency matrix. Second, a graph attention autoencoder is designed to enhance feature discriminability by leveraging an attention mechanism to fuse multi-hop neighborhood information. Furthermore, a dynamic structure optimization strategy based on node similarity is proposed to periodically update the adjacency matrix and capture the evolving similarities among nodes. Finally, a self-supervised clustering module is incorporated to improve the synergy between feature representation and clustering performance by optimizing cluster distribution alignment via KL divergence. Extensive experiments on six public datasets, including ACM, DBLP, CITESEER, and TEXAS, demonstrate that the proposed AWDGC significantly outperforms eight representative baseline methods across various clustering metrics.