How is the theme of darkness developed in Act II of Shakespeare's Macbeth?

Darkness is a theme that drives the plot development in Act Two of Shakespeare's Macbeth.

The Elizabethans believed firmly in several things: that God ordained who was to reign on the throne. If the king was murdered, order in the universe was disrupted, and unnatural things (in nature and the spirit realm) would take place. They also firmly accepted the existence of witches, demons, fairies, changelings, etc. The presence of the supernatural (anything beyond the natural world—even God) was uppermost in their minds, but most especially at night because Elizabethans believed that evil had the upper-hand after dark; and darkness was a time of death. There can be no doubt that Macbeth's plan to murder his friend, king, cousin, and houseguest moves along swiftly with elements (literal and figurative) of darkness.

In Macbeth, in scene one, Banquo notes that the natural mind is haunted by "cursed thoughts" when one tries to sleep (9). Banquo feels a "summons" weighing down on him (the supernatural), preventing him from sleep—perhaps warning him (7-8). Banquo encounters Macbeth who says he cannot sleep, but the audience is also aware that Macbeth is plotting to kill Duncan as he sleeps that night. 

Banquo tells Macbeth that the night before, he dreamed of the witches (24). The witches originally appeared on a dark and gloomy day, and are associated with darkness, in general. Darkness also evokes a sense of what is hidden and/or deceit. Mention of the Weird Sisters places the witches, like an eerie specter, between the men—showing a clear separation between these once-devoted friends. (This sense was not present after the witches first spoke to Banquo and Macbeth, but have only arisen since Macbeth has plotted with his wife to commit murder based on their predictions.) Taking place also in these scene of darkness, Macbeth tries to get Banquo's support as he prepares for the discovery of Duncan's murder: he tells Banquo that if he backs Macbeth when the time is right, he will make it worth Banquo's while. Macbeth tries to trick Banquo into supporting him before the murder is discovered—a deceitful move on Macbeth's part.

After they split up, Macbeth sees a spectral dagger in front of him.

Is this a dagger which I see before me,
The handle toward my hand? (41-42)

Macbeth sees the ghostly dagger showing him (he imagines) a path to the King's door. This is the hand of the supernatural, present because Macbeth has chosen to involve himself with the witches.

Macbeth describes what occurs in the darkness of night—when evil reigns:

Now o'er the one half-world
Nature seems dead, and wicked dreams abuse
The curtain'd sleep; witchcraft celebrates
Pale Hecate's offerings; and wither'd Murder,
Alarum'd by his sentinel, the wolf,
Whose howl's his watch, thus with his stealthy pace,
With Tarquin's ravishing strides, towards his design
Moves like a ghost. (57-64)

Notice words and phrases like "dead," "wicked," "abuse," "witchcraft celebrates," "Hecate's offerings," and "wither'd Murder," among others, which help to set the mood of darkness and death. All of these things take place in the night. By the cover of darkness, Macbeth will defy even God.

In scene two, Lady Macbeth hears the owl—a harbinger of death:

It was the owl that shriek'd, the fatal bellman,
Which gives the stern'st good-night. (4-5)

While the grooms sleep under the influence of Lady Macbeth's drugged wine, they mumble of "murder" and say prayers as they sleep, which echoes Banquo's earlier musing of how wickedness attempts to come into the mind as one sleeps. This is also the scene when Macbeth notes that after the murder, he heard a voice say:

Glamis hath murdered sleep, and therefore Cawdor
Shall sleep no more. Macbeth shall sleep no more. (54-55)

Because he has killed Duncan as he slept, Macbeth is (he thinks) cursed to sleeplessness. As scene three begins, there is a knocking at the gate, as Macduff comes to collect Duncan, taking leave of Inverness. It is daylight and Macbeth arrives to welcome Macduff and Lennox. While Macduff goes to report to Duncan, Lennox reports of unnatural occurrences that took place the night before:

Our chimneys were blown down, and, as they say,
Lamentings heard i’ the air, strange screams of death,
And prophesying with accents terrible
Of dire combustion and confused events... (56-59)

A moment later, as the light has arrived with daybreak, so has the knowledge of Duncan's murder, as Macduff reenters. 

The darkness of the first two scenes of the play provide a cover under which unnatural things take place: it is in the darkness that evil reigns, when men are susceptible to "cursed thoughts" in their sleep, when murder takes place, and when the natural balance of the universe is disrupted and the world is thrown into chaos.

It is the darkness of Macbeth's heart that allows him to carry out Duncan's murder. It is the darkness in Lady Macbeth that allows her to return the daggers to the dead grooms to throw the blame upon them. Lastly, it is in the darkness that the world is opened to chaos and mayhem from creatures such as Hecate and the three witches. The darkness is literal, in terms of nightfall and evil practices, but it is also figurative with regard to the hearts of Macbeth and his wife.