Favoriting tweets in Twitter is not the same as liking something on Facebook. When you click on the star on a tweet you are saving the tweet for later. When you favorite a tweet the person who tweeted it is notified in their notifications. If you are trying to tell the person you like their tweet rather than save their tweet for later, I suggest you retweet their tweet or reply with a “thank you for this tweet” instead of favoriting it.
Find Your Favorites
Click on yourself! Click on the “Home” icon along the top. Click on your name. The statistics of how many tweets, following, followers, favorites and lists are live hyperlinks. Click on the number of favorites to see your list of favorite tweets!