Physics textbook authors commonly introduce the concept of weightlessness (apparent or real) through a "thought experiment" in which a person weighs herself or himself in an elevator. When the elevator falls freely, the spring balance should show zero weight. There is an unresolved controversy about how this "zero reading" comes about. Drawings in some books, the first of which appeared in a book of Perelman 80 years ago, show that the person continues to be in contact with the balance. It means that "zero weight" arises as a consequence of "the fact" that the falling person and balance, although in contact, do not press on each other. Drawings in other books, among them those elaborated by NASA, represent the person and the balance launched upward and floating separately in midair. Using a homemade "falling box" with attached video camera, we did initial experiments for a very simplified but basically similar situation. The results that we obtained suggest that, in a free-falling elevator, a real balance would hardly launch a person upward.