User blog comment:Waters Knight/Weiss killed 'herself' in the White Trailer/@comment-9090085-20131219002528/@comment-3146930-20131219004054

For me, the obvious answer is that Weiss isn't that skilled in Aura or her Aura isn't strong enough to heal in injury that was obviously large and deep. I mean we saw Jaune's Aura heal a cut on his cheek, but he has been mentioned as having a large amount of Aura and the cut was small. Weiss on the other hand relies mostly on her Semblance, the ability to make Glyphs. So if she hasn't trained in using her Aura, it could be weak and unable to heal a devastating cut.

That was longer then I was planning...short answer: For me, the obvious reason was that her Aura isn't or wasn't strong enough to heal the injury, thus causing the scar. It isn't like Aura can fix everything.