What does the word "double" signify in Macbeth?

There are a number of words that appear obviously as motifs in Macbeth (blood, sleep, etc.). The word "double" is also a motif, though it doesn't seem to get quite the amount of attention that other, more concrete/tangible words get in analysis. 

The word "double" appears in both literal and abstract form in the play. It appears literally when the witches describe their plans: "Double, double toil and trouble" (Act 1, Scene 1), where they mean to literally double the trouble that is about to happen. First, they use the word twice (doubling it); the punctuation of the sentence makes the word appear as a repetitive device. Also, the witches are troublemakers, and they like to cause as much difficulty for their targets as possible. By doubling, in this case, Macbeth's trouble, they get to experience double the amount of glee at watching the consequences.

Another literal use is from the Captain as he describes the battle in Act 1, Scene 2. "As cannons overcharged with double cracks / So they doubly redoubled strokes upon the foe." This helps to show the force and height of the battle: the cannons were packed with double the ammunition, and the soldiers "doubly redoubled," meaning they possibly quadrupled their physical efforts (shots, stabs, etc.) on the opposition.

Beyond the literal meanings, the word "double" has an abstract meaning as well that contributes to one of the main themes of Macbeth: the idea that things are not as they seem to be. More specifically, the word suggests that, though Macbeth appears to act with confidence, he actually spends the entire play becoming weaker and more dependent on those around him. 

"He's here in double trust," Macbeth says to describe King Duncan and his visit to Inverness in Act 1, Scene 7. This shows that Macbeth is already feeling guilt, though his actions suggest otherwise. It's impossible to "double trust"; either you trust someone, or you don't. Though Macbeth tries to use the word, in this case, literally (Duncan sees Macbeth as both a subject and as a host), the subtext suggests Macbeth is actually feeling twice the guilt over what he is about to do.

This idea continues toward the conclusion of the play (Act 4, Scene 1) when Macbeth makes the decision to kill MacDuff. "Then live, Macduff. What need I fear of thee? / But yet I’ll make assurance double sure, / And take a bond of fate." There is no need to touch MacDuff; he is not a threat to Macbeth's future. Yet, Macbeth is now mired in the witches' prophecies so deeply, he's compelled by guilt and dependence on the witches' words to "make double sure." (Again, like trust, one cannot be "double" sure; you're either sure, or you're not).

Though other words in Macbeth often receive more attention for their literal, concrete qualities, the word "double" contributes significant meaning to the play; looking for recurrences of this word can double the reader's enjoyment and understanding of the text.