The balrog in the movie is plainly a juvenile. There are only two horns, and the hoofs are underdeveloped. The wings are still ethereal shadow, rather than the full-grown functional ones the adults sport in Silmarillion.
Most importantly, it is somewhat unstable and emotionally overwrought. It is unsure whether to attack the company at all, judging by the time it takes to get at them. A mature balrog would have caught them all before they got out of that multi-columned hall, but this one rather shyly (and endearingly) hid behind the columns, and meandered through Moria, barely making it to the Bridge in time to catch Gandalf.
Ah, the Bridge of Khazad-dum! How many young dwarves and dwarf-maidens hurried back over it into the Palace after a late night out spooning down by the Mirrormere? Little used as a defense since the First Age, it had become THE romantic spot of all of Dwarrowdelf. Could you indulge in one last immodest embrace and also keep from falling to your doom? That was a challenge met by many, and failed by some, throughout the great years of Khazad-dum.
The Balrog, poor thing, knew this. Its elders, deep in the bowels of the Mines, kept alive the poetic and romantic traditions of the Dwarves, although the Dwarves themselves had long ago been charred into pencil lead.
The conclusion is obvious: our Balrog was a female, a girl, a blossoming beautiful adolescent Balrogette of some 800 years or less. Raised to consume all mortal trespassers in gouts of hell-fire, she had instead fallen in love with love, and longed for that death-defying embrace that proved one's devotion, on the center of a 3-foot wide stone bridge over a 10-mile-deep abyss.
Gandalf. Not a young man. But shot through with Power, with the Flame of Anor. It seemed so right. She stepped forward, she offered her Flame of Udun.
He, misunderstanding, rejected her. Puzzled, she blew him a fiery kiss. He, unaccountably, showed fear and said NO, Let's Just Be Friends in a tongue only an Elven blade of Gondolin can speak.
Rage overtook her. Balrogs are not calm creatures even in maturity. She determined to hug him if it killed her and him -- and it did. She achieved her wish, even as she and he joined the unhappy toll of lovers who failed the test of the Love-Span of Moria, of Khazad-dum (literally, "Kissing Doom").