A set of scales stood in entrance of the cliffside cave that held the candidates' names. Before Sawyer and the Man in Black's visit in "The Substitute", two rocks, one black and one white, roughly balanced the scales. The Man in Black then threw the white rock in the ocean, tilting them in the remaining black rock's favor. He referred to this as an "inside joke".
Jacob and the Man in Black used to play senet using black and white rocks when they were children, and they returned to the game throughout adulthood. During their centuries of rivalry following the Man in Black's transformation, they traded stones to symbolically keep score. Jacob sent his brother a white stone in 1867 after thwarting an attempt on his life and recruiting Richard. The Man in Black, later seen with the stone, commented on Jacob's "gloating". ("Ab Aeterno")
The paintings seen in Charles Widmore's office in a flash sideways
Dogen told Sayid that for every man there is a scale; on one side of the scale there is good, and on the other side, evil. ("Sundown")
The astrological symbol for Libra is a set of scales. Libra is the seventh sign of the Zodiac, and it begins on September 23 - the day after the crash of Oceanic 815.
The scales are one of the traditional symbols of justice, as wielded by statues of Lady Justice. This corresponds to the use in metaphor of matters being "held in the balance". It has its origins in ancient Egypt.