I'm not quite sure what you mean by "included in the application", since you can potentially deliver any library as long as licensing is allowed. Do you mean the fact that sqlite is small or that it is a public domain ?
Mercurial is a similarly lightweight version control software. If you are writing your application in python, which is probably since python now includes sqlite3 , importing functions directly from mercury source code should not be too complicated, otherwise there is no shame in invoking command line processes, although it may be more clunkier. Mercurial is not publicly available, but it is GPL'd.
Mercurial is also my personal favorite among modern version control systems. It jumps ahead of CVS and Subversion and is very similar to GIT, but somewhat easier to use.
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