[Pitchwife]

I guess range would be the crucial issue.
The Balrog of Moria is described as being "of man-shape maybe, yet greater". So the Balrog would have all the time in the world to hit the Dwarf with its whip or sword before the Dwarf could get close enough to make a dent.
Now, when you're facing an enemy much taller than yourself, I'd say the only viable tactic is trying to dodge their blows and closing in, aiming for the knees (like Merry did against the Witch-King) in order to cripple them and bring them down so you can chop them up at leisure. If the Dwarf was agile enough, he might stand a chance. Durin VI, however, obviously wasn't.
Which makes me wonder... When the Dwarves of Moria first stirred up Durin's Bane, it probably didn't have a host of Orcs and Trolls at its disposal as in the Moria chapters of LotR. How come the entire Dwarven host of Moria couldn't deal with a single Balrog in an organized attack? After all, the Dwarves of Belegost managed to drive Glaurung himself from the field in the Nirnaeth Arnoediad; and a fire-breathing dragon seems to me a much more formidable enemy than a Balrog. Looks like Dwarvish fighting prowess had deteriorated somewhat since the First Age...