This paper considers one-hop device-to-device-assisted wireless caching networks that cache video files of varying quality levels, with the assumption that the base station can control the video quality but cache-enabled devices cannot. Two problems arise in such a caching network: file placement problem and node association problem. This paper suggests a method to cache videos of different qualities, and thus of varying file sizes, by maximizing the sum of video quality measures that users can enjoy. There exists an interesting tradeoff between video quality and video diversity, i.e., the ability to provision diverse video files. By caching high-quality files, the cache-enabled devices can provide high-quality video, but cannot cache a variety of files. Conversely, when the device caches various files, it cannot provide a good quality for file-requesting users. In addition, when multiple devices cache the same file but their qualities are different, advanced node association is required for file delivery. This paper proposes a node association algorithm that maximizes time-averaged video quality for multiple users under a playback delay constraint. In this algorithm, we also consider request collision, the situation where several users request files from the same device at the same time, and we propose two ways to cope with the collision: scheduling of one user and non-orthogonal multiple access. Simulation results verify that the proposed caching method and the node association algorithm work reliably.