Answer

This is a question that is related to the site, since it comes up in the Talmudic passage about the obligation to tip the scale a handbreadth in Bava Batra 88b, and there in the Talmud. It is indeed a puzzling passage, and many years ago I went around with it among the great rabbis of Bnei Brak and did not receive a satisfactory answer.
This of course depends on how the scales are built. If the scales are a horizontal bar with two pans hanging from its two ends, then they should remain wherever you place them (and not balance into a horizontal line), since the forces and torques are equal on both sides in any position. But as I recall, Rashbam there explains that the scales are built in the shape of a chet (that is, there is a slight drop downward on both sides), and if so then they should balance horizontally. But there are other medieval authorities in which it appears that we are talking about a straight bar, and then this is simply a mistake.