Favorite data is not exactly confidential; I can go to a user's profile and see everything they have as a favorite. Why isn't there an easy way to see who marked my questions as favorite?
My guess is that you could probably work up a query with some SQL-fu.
This site is usually pretty easy to work with:
You could query the database:
There's no way to do this directly (Stack Overflow provides no mechanism to do so), but sometimes you can use Google to find out. As an example, suppose you wanted to find out who marked "Jon Skeet Facts?" as favorite. Just search for
"Jon Skeet Facts?" site:stackoverflow.com inurl:favorites
It looks like you may be able to get this from the public data dump now, starting from the July 2009 dump: https://blog.stackoverflow.com/2009/07/creative-commons-data-dump-july-09/