Given increasing demand for very large format contents and displays, spatial resolution changes have become an important part of video streaming. In particular, video downscaling is a key ingredient that streaming providers implement in their encoding pipeline as part of video quality optimization workflows. Here, we propose a downsampling network architecture that progressively reconstructs residuals at different scales. Since the layers of convolutional neural networks (CNNs) can only be used to alter the resolutions of their inputs by integer scale factors, we seek new ways to achieve fractional scaling, which is crucial in many video processing applications. More concretely, we utilize an alternative building block, formulated as a conventional convolutional layer followed by a differentiable resizer. To validate the efficacy of our proposed downsampling network, we integrated it into a modern video encoding system for adaptive streaming. We extensively evaluated our method using a variety of different video codecs and upsampling algorithms to show its generality. The experimental results show that improvements in coding efficiency over the conventional Lanczos algorithm and state-of-the-art methods are attained, in terms of PSNR, SSIM, and VMAF, when tested on high-resolution test videos. In addition to quantitative experiments, we also carried out a subjective quality study, validating that the proposed downsampling model yields favorable results.