Few-shot learning is a nascent research topic, motivated by the fact that traditional deep learning requires tremendous amounts of data. In this work, we propose a new task along this research direction, we call few-shot common-localization. Given a few weakly-supervised support images, we aim to localize the common object in the query image without any box annotation. This task differs from standard few-shot settings, since we aim to address the localization problem, rather than the global classification problem. To tackle this new problem, we propose a network that aims to get the most out of the support and query images. To that end, we introduce a spatial similarity module that searches the spatial commonality among the given images. We furthermore introduce a feature reweighting module, which balances the influence of different support images through graph convolutional networks. To evaluate few-shot common-localization, we repurpose and reorganize the well-known Pascal VOC and MS-COCO datasets, as well as a video dataset from Imagenet VID. Experimental evaluation on the new settings for few-shot common-localization shows the importance of searching for spatial similarity and feature reweighting, outperforming baselines from related tasks.