What actions did Thomas Becket do to limit the king's powers in the movie Becket?
Henry II and Thomas a Becket are friends and drinking buddies until Henry appoints Thomas as Archbishop of Canterbury making him the head of the Church in England. The two most powerful organizations at the time are the King and the Church. The King needs money for his various wars and conquests, and he assumes that by appointing his best friend to the head of the Church, he will get it.
But rather than give the king the ally he is looking for, the appointment creates a rival. The office changes Becket; against odds it gives him something to believe in, and he makes the kind of principled stand for the rights of the church that the king cannot abide, even in his best friend.
Becket becomes a favorite of the common people by giving them his cast off cloaks and making sure they have shoes and food for the winter months. He becomes a man of conscience and refuses to fork over the church's money to fund Henry's projects. Becket becomes more favored and popular than Henry himself and Henry recognizes his problem, so he utters, "Will no one rid me of this meddlesome priest?" His knights hear him and take him at his word. They murder him in the cathedral at Canterbury which is why the pilgrimage to Canterbury began and still continues today--to pay the people's priest homage.