Why does Macbeth seek the witches in Act III?
Macbeth wishes to seek out the witches, in Act III (scenes i and iiii). Macbeth discusses the reasons as to why.
Upon my head they placed a fruitless crow, And put a barren sceptre in my gripe, Thence to be wrench'd with an unlineal hand, No son of mine succeeding. (Act III, i)
Here, Macbeth discusses the part of the witches' prophecy that has come true. Macbeth has become king. But, he worries about what else he must do to keep his crown given that he will not have any sons to pass the crown to. Another part of the prophecy states that the crown will go to someone outside of Macbeth's lineage.
And betimes I will, to the weird sisters: More they shall speak, for now I am bent to know, By the worst means, the worst. (Act III, iii)
Here, Macbeth states his intent to go back to the witches and ask them of his future. He is concerned about what he has done to this point to gain the crown; his concern, now, lies in what he must do to keep the crown.
In Act Three, Scene 4, Macbeth learns that Fleance escaped the assassins, which disturbs and worries him. He is no longer confident that he will cement his reign as King of Scotland for an extended period of time and fears that Banquo's descendants will still inherit the throne. Later on in the scene, Macbeth sees Banquo's ghost at the banquet, which further increases his anxiety. When the Scottish lords leave the banquet, Macbeth tells his wife that he will visit the Three Witches again in order to learn more about his future. At this point in the play, Macbeth is concerned about his own well-being and is motivated to consult the witches again in order to discover more about his destiny. Essentially, Macbeth expresses his desire to visit with the witches again in order to obtain information concerning his security and whether or not he will retain power as King of Scotland for an extended period of time.
He wants to know about his future and wants to know if he would get the crown after killing Duncan but the witches show him that there is someone else coming in his way.
He seeks the witches because he is power-hungry and the witches had told him prophecies before, so he wants to find out more information. Also, because Fleance got away, he is paranoid.