If your files are mostly text, Git will be much smaller than twice your data. For example, I save Vim configuration files in a Git repository so that I can easily get them anywhere and keep them up to date. The configuration files themselves are a little less than 3 MB, and the .git directory for this is only a little more than 1 MB after fixing 683. It is smaller than the Subversion check and is small enough not to worry.
It used to be necessary to run git gc in the repository so often in order to trim unreachable data from the repository. This was especially true after many rearrangements or other editing of the story. But since it’s around Git 1.5, it keeps track of the amount of unreachable data as it progresses and automatically reduces it when it gets too much. There are configuration options to configure it if you really have little space, as well as CPU time and cycles. See git help gc more details, but I really think you just won't find a problem in space.