Saturn was designed from the ground up to be as lightweight and use as little storage as possible. As of version 0.1.2, Saturn uses 1.76 Megabytes of storage space. Saturn also uses approximately 14 Kilobytes of database space.
However, this may vary slightly depending on certain factors such as file system, website assets, name, description, etc.
This amount will increase as your website gains more content. The currently largest confirmed Saturn file size is 40.1 Megabytes (About 3.1 Megabytes if you don't count their homepage video) and the database size is 142 Kilobytes, owned by GeolHistory.org