BuddyPress.org

Not sure exactly what you mean here, but you might want to look at the Curator plugin here: http://wpebooks.com/curator/ to select posts from users blogs. I’m thinking you aren’t running a multisite install though, so another option would be somehow capture an RSS feed of your “favorites” and then feed them back to the blog. You would need to be very purposeful about your use of the Favorites button, but it seems that an RSS feed exists at domain.com/members/username/activity/favorites/feed (I haven’t tested this too deeply, but adding the word feed to the end of that URL opened up a listing of my favorites in a feed reader) that you could feed back into your blog with something like this https://wordpress.org/extend/plugins/feedwordpress/ to create the combination. Alternatively you could use the RSS Widget to highlight favorite videos on the sidebar.