Personally, I mostly use favouriting tweets for my own personal needs only - to bookmark some things. My behaviour would be unchanged if favouriting became private and no one was notified that I favourited their tweet.

Sometimes, if I really like a tweet, I'll favourite it because I have no other way to say +1 (other than replying to it). But I must like it enough to want to sacrifice the integrity of my bookmarks.

Based on what I'm reading here, it seems that people have wildly varying ways in which they use favouriting.