Weakly supervised video grounding aims to localize temporal boundaries relevant to a given query without explicit ground-truth temporal boundaries. While existing methods primarily use Gaussian-based proposals, they overlook the importance of (1) boundary prediction and (2) top-1 prediction selection during inference. In their boundary prediction, boundaries are simply set at half a standard deviation away from a Gaussian mean on both sides, which may not accurately capture the optimal boundaries. In the top-1 prediction process, these existing methods rely heavily on intersections with other proposals, without considering the varying quality of each proposal. To address these issues, we explore various inference strategies by introducing (1) novel boundary prediction methods to capture diverse boundaries from multiple Gaussians and (2) new selection methods that take proposal quality into account. Extensive experiments on the ActivityNet Captions and Charades-STA datasets validate the effectiveness of our inference strategies, demonstrating performance improvements without requiring additional training.