[Gwathagor]

I take Tolkien's statement that the Witch King received added demonic force to mean an increased demonic force. In other words, the power that was added to was the power which the Witch King made the most frequent and effective use of; that is, the fear and terror that he inspired. That is his primary function, even as the leader of Sauron's armies.

No WAY is the Witch King's scaring-power going to work on a balrog which derived his power directly from Morgoth, the OG himself.