For Artifactory version 3.1.1 and above, the information on disc-memory usage and a breakdown of how much space is used by each of the repositories is available on the 'Storage Summary' page in the UI at Admin tab ? Advanced ? Storage Summary.
If you want specific information regarding a sub-folder inside a given repository, or if you are using a version of Artifactory older than 3.1.1, you can use the 'repoStats' user plugin. With this plugin, you can specify any path within a repository to get it's artifact count and size. If you need additional/altered, functionality in the plugin, you can edit it to adjust it to your own needs. Please refer to our user plugin documentation and our public API, for further information on this subject.