Balance (scales) dream meaning is explained below using 2 different sources. Each interpretation is shown with its source.

Interpretation 1 — Patrica Telesco

(see Dieting, Weight)

How does this tool appear? Is it lopsided? If so, consider if you have been stressing certain things too much in your life, resulting in throwing everything else off kilter.

An alternative emblem for the zodiac sign of Libra, whose name literally means balance.

The counsel of this image is using perspective and fairness to reach a harmonious decision in whatever situation lies heavy on your heart.

The quality of living. In ancient Egypt, the souls of the recendv departed were weighed for worthiness on a scale against Maat’s feather. Maat was the Mother of All Truth. Similarly, in ancient Greece, Hermes weighed souls at the throne of Zeus, and among Christians, the archangel Michael assumed this role.

Equity especially in legal matters. In the Tarot, the Justice card carries a balance to ensure impartiality.

The amount of figurative weight you carry in terms of responsibility, burdens, etc.

Source: The Language of Dreams Author: Patrica Telesco

Interpretation 2 — Cafer-i Sadik

interpreted upon 6 sides: judge, scholar, jurist, engineer & worthy decision / ruling & crooked decision. Saw: child or sister, or brother, or partner. And whoever sees himself cutting something with a saw then he will triumph. And cutting wood is [interpreted as] victory with the enemies.
Source: Islamic Dream - Cafer-i Sadik Author: Cafer-i Sadik