I seem to recall somewhere in the reading that the Valar originally didn't have shape like we do, but they took on shape in order to converse with the Children of Iluvatar more easily. Remember in the Lord of the Rings, how Sauron is said to have been able to seem wise and noble for a long time? An example of this is when he was helping the Elves craft the Rings of Power. We also see in the tale of Beren and Luthien that he turns into a great wolf, and then into a snake, and atlast into a vampire.
The Valar and Maiar could change their appearance like this unless they expended so much of their power that they got 'stuck' with a certain shape. This eventually happened to both Morgoth and Sauron.
I'd say the Balrogs just chose to appear like that, for the intimidation factor I guess. To back up this theory, remeber Gandalf's account of his fight/fall with the Balrog, how he turned into "a thing of slime, stronger than a strangling snake."
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