content: If you have an Android phone, though, they already know that it's your handset; they aren't stupid. Two-factor auth just makes sure that it's you trying to log in to your account, by using your phone as a type of physical key that unlocks your Gmail. They have your data, either way; unless you have a non-Android phone and don't log in to different Google services from the same IP-address using your various devices. If you're already using an Android phone, you'd might as well enable two-factor auth.