The Balrog made no answer.  The fire in it seemed to die, but
  the darkness grew.  It stepped forward slowly on to the bridge,
  and suddenly it drew itself up to a great height, and its wings
  were spread from wall to wall; but still Gandalf could be
  seen, glimmering in the gloom; he seemed small, and altogether
  alone: grey and bent, like a wizened tree before the onset of
  a storm.

That's the clencher. Take it or leave it.

Just please don't come back and say it couldn't have had wings because Tolkien wrote "and the shadow about it reached it LIKE two vast wings". If that phrase means there were no wings, then there was no shadow, because Tolkien wrote "what it was could not be seen: it was LIKE a great shadow".

And if there was no shadow, then nothing could have stretched out LIKE two vast wings. Hence, the wings were there because the shadow was there.
------------------
Xenite.Org: Science Fiction and Fantasy