scale
the scales fall from someone's eyes someone is no longer deceived.
☞ In the Bible, this expression described how St Paul, blinded by his vision on the road to Damascus, received his sight back at the hand of God (Acts 9:18).
throw something on (or into) the scale emphasize the relevance of something to one side of an argument or debate.
tip (or turn) the scales (or balance): seetip.
tip (or turn) the scales at have a weight of a specified amount.