Weakly supervised visual grounding aims to predict the region in an image that corresponds to a specific linguistic query, where the mapping between the target object and query is unknown in the training stage. The state-of-the-art method uses a vision language pre-training model to acquire heatmaps from Grad-CAM, which matches every query word with an image region, and uses the combined heatmap to rank the region proposals. In this paper, we propose two simple but efficient methods for improving this approach. First, we propose a target-aware cropping approach to encourage the model to learn both object and scene level semantic representations. Second, we apply dependency parsing to extract words related to the target object, and then put emphasis on these words in the heatmap combination. Our method surpasses the previous SOTA methods on RefCOCO, RefCOCO+, and RefCOCOg by a notable margin.