Accurate prediction of drug target affinity (DTA) is critical for accelerating drug discovery, yet existing methods often struggle with topological diversity and insufficient feature extraction in molecular graphs. This paper proposes a novel framework, Topological Adaptive Weighted Drug Target Affinity Prediction (TAW-DTA), which integrates a Topological Adaptive Graph Convolutional Network (TAGCN) and a gated skip-connection mechanism to address these limitations. TAGCN dynamically adjusts convolution filters based on node topology, enabling robust feature extraction from drug molecular graphs and weighted protein contact maps. The gated skip-connection mechanism mitigates gradient vanishing and feature degradation in deep networks by selectively fusing multiscale features. Evaluations of benchmark data sets demonstrate state-of-the-art performance, with improvements in the concordance index (CI) and reduced prediction errors. Ablation studies confirm the efficacy of TAGCN and the skip-connection mechanism. This framework offers a scalable and interpretable solution for DTA prediction, with significant potential for practical drug development applications.