You may like to know who favorites your tweets for several reasons. For example, people usually favorite tweets in their timeline that they like the most and want to use as bookmarks for future references. So, by checking what people like to read, you may keep posting more of such tweets and gain more followers, though there may be several other reasons you may like to know what tweets are favorited by your followers.
Using a free service – Favotter, you can check who favorites your tweet. Best part is you need not ever create an account or signup with the service, just visit the page and enter your twitter handle to check out who favorites your tweets. Well, as its not login based service, if your tweets are protected then you may not be able to use this service.