What do the the twofold balls in the king's hand indicate?
Since the Tudor Queen Elizabeth died childless, King James VI of Scotland a Stuart was crowned the King of England as King James I. Two coronations were held, one in Scotland where one scepter was used and one in England where two scepters were used: "That two-fold balls and treble scepters carry." Scholars also interpret "treble scepter" to mean that King James' coronation united the three kingdoms of Scotland, England and Ireland.
In the show of eight kings in 'Macbeth', act4 sc.1, the witches give Macbeth a pre-view of the long line of kingship that Banquo's successors would enjoy. It is here in Macbeth's confused response to the show that he refers to some 'that two-fold balls and treble sceptres carry'. The 'two-fold balls' in the hand of the king may be a reference to the union of the crowns of England and Scotland under king James I, or it may also be the two coronations of James VI in Scotland and of him again as James I. The first explanation seems to me more meaningful and more appropriate.