Notes to Macbeth, Act 2, Scene 3, lines 8-11: "an equivocator . . . to heaven"
swear in both the scales against either scale: i.e., hypocritically vow support for either side in a controversy. The metaphor refers to the type of balance beam scale often used as a symbol of justice. Each side of the scales has one scale, which is a pan to hold either the weights or the material to be weighed.
who committed treason enough for God's sake, yet could not equivocate to heaven: This passage is often considered to be a reference to Henry Garnet, a Jesuit of Shakespeare's time who wrote a "A Treatise of Equivocation," and who was executed for treason. He wrote the "Treatise" in order to tell other Catholics how to deal with dangerous questions from Protestant inquisitors. If the Catholics admitted that they were Catholics, they would be in serious trouble with the Protestants. On the other hand, it was a sin against God to lie under oath. The solution to the problem, Garnet said, was equivocation. Following is an example of a saint who equivocated for God's sake:
[An] anecdote often used to illustrate equivocation concerns Francis of Assisi. He once saw a man fleeing from a murderer. When the murderer then came upon Francis, he demanded to know if his quarry had passed that way. Francis answered, "He did not pass this way," sliding his forefinger into the sleeve of his cassock, thus misleading the murderer and saving a life. Wikipedia: Mental reservation.
Equivocation is also a theme in the play. See Macbeth Navigator page on equivocation.