The existing research in action recognition is mostly focused on high-quality videos where the action is distinctly visible. In real-world surveillance environments, the actions in videos are captured at a wide range of resolutions. Most activities occur at a distance with a small resolution and recognizing such activities is a challenging problem. In this work, we focus on recognizing tiny actions in videos. We introduce a benchmark dataset, TinyVIRAT, which contains natural low-resolution activities. The actions in TinyVIRAT videos have multiple labels and they are extracted from surveillance videos which makes them realistic and more challenging. We propose a novel method for recognizing tiny actions in videos which utilizes a progressive generative approach to improve the quality of low-resolution actions. The proposed method also consists of a weakly trained attention mechanism which helps in focusing on the activity regions in the video. We perform extensive experiments to benchmark the proposed TinyVIRAT dataset and observe that the proposed method significantly improves the action recognition performance over baselines. We also evaluate the proposed approach on synthetically resized action recognition datasets and achieve state-of-the-art results when compared with existing methods. The dataset and code is publicly available at https://github.com/UgurDemir/Tiny-VIRAT.