Using "too" at the end of the sentence

Both are correct. They can have different meanings.

You are my favorite person, too.

or

You are my favorite person too.

This adds to a previous statement. Perhaps the addressee had told the speaker that he was his favorite person. Or perhaps the speaker had said that the addressee is a third party's favorite person. Or it can mean the same as…

You too are my favorite person.

This means that the addressee, in addition to someone already mentioned, is the speaker's favorite person. This would be highly unusual since people don't speak of different two people as "my favorite person" (they might say "among my favorite people").