Weakly supervised visual grounding (VG) aims to locate objects in images based on text descriptions. Despite significant progress, existing methods lack strong cross-modal reasoning to distinguish subtle semantic differences in text expressions due to category-based and attribute-based ambiguity. To address these challenges, we introduce AlignCAT, a novel query-based semantic matching framework for weakly supervised VG. To enhance visual-linguistic alignment, we propose a coarse-grained alignment module that utilizes category information and global context, effectively mitigating interference from category-inconsistent objects. Subsequently, a fine-grained alignment module leverages descriptive information and captures word-level text features to achieve attribute consistency. By exploiting linguistic cues to their fullest extent, our proposed AlignCAT progressively filters out misaligned visual queries and enhances contrastive learning efficiency. Extensive experiments on three VG benchmarks, namely RefCOCO, RefCOCO+, and RefCOCOg, verify the superiority of AlignCAT against existing weakly supervised methods on two VG tasks. Our code is available at: https://github.com/I2-Multimedia-Lab/AlignCAT.