Most video platforms provide video streaming services with different qualities, and the resolution of the videos usually adjusts the quality of the services. So high-resolution videos need to be downsampled for compression. In order to solve the problem of video coding at different resolutions, we propose a rate-guided arbitrary rescaling network (RARN) for video resizing before encoding. To help the RARN compatible with standard codecs and generate compression-friendly results, an iteratively optimized transformer-based virtual codec (TVC) is introduced to simulate the key components of video encoding and perform bitrate estimation. By iteratively training the TVC and the RARN, we achieved 5%-29% BD-Rate reduction anchored by linear interpolation under different encoding configurations and resolutions, exceeding the previous methods on most test videos. Furthermore, the lightweight RARN structure can process FHD (1080p) content at real-time speed (91 FPS) and obtain a considerable rate reduction.