Remember when I said that "Mirror, Mirror" was one of the good songs on the soundtrack? Honestly, it's probably the best. The lyrics are minimal (and mediocre), so the story, instead, is told through the animation that goes with it: The White Trailer. The message is obvious: Weiss is your typical lonely rich girl, jaded because of the pressure to be perfect. Of course, why should I explain it when TVTropes found the most fitting person to describe the emotional impact?
Of course, you don't need interesting character traits or stories to make these fans feel sad.
Aww, she got turned down. So tragic! So depressing! So... insignificant in its affect on anything in the show. This scene lasts two seconds at best. It's supposed to be funny. Guess not.