Cool! I just had to try it. A penny may / may not have been just the right mass, and I used a slightly heavier than average grade of paper. But it was sort of stable.
When I drop it, the front corners bend upward. This increases the drag at the front end. This seems to be the source of the bend you show. The nose comes up and the plane slows.
Sometimes it is stable. Sometimes the nose goes too far up, it stalls, and then the nose drops. If you drop it down some stairs, it has more time to develop unstable behavior.
