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.
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.