Julius Caesar was considerably older than Mark Antony, and their relationship was somewhat like that of a father and son. Shakespeare makes it clear than Antony was always respectful and obedient towards Caesar. For example, when Caesar tells him to be sure to touch Calpurnia when he is running the ceremonial race, Antony says:
I shall remember:
When Caesar says "Do this," it is performed.
Caesar's sudden death leaves a power vacuum in Rome, as it does whenever any powerful man is removed from the scene. Antony has been subservient and self-effacing up to the time of the assassination, but then he demonstrates some of his previously hidden character traits and hidden talents. He is forced into doing this out of sheer necessity. He knows that his best course of action is to help Octavius claim Caesar's place. No doubt Antony is thoroughly familiar with the terms of Caesar's will before he reads it to the mob during his funeral oration. Antony was Caesar's right-hand man. He has learned a great deal from his mentor and can act wisely, decisively, and courageously.
Brutus does not appreciate Antony's strength of character. Antony very judiciously sends a messenger to Brutus with instructions to kneel and then prostrate himself when he delivers his master's message in Act III, Scene 1. The messenger's body language is intended to symbolize Antony's own humility and assumed impotence and helplessness without the guidance and aegis of the great Julius Caesar.
But Antony is rapidly developing into a man of extraordinary strength of character as a result of all the factors that have combined to make him become independent and self-reliant. These factors include fear for his own life, grief at the loss of his great friend and father-figure, hatred for Caesar's murderers, a strong desire for revenge, and a desire to take advantage of this opportunity to become one of the new leaders of the Roman people, the Roman legions, and the Roman empire.
Although Brutus does not see Antony's true colors, Cassius has feared and mistrusted him as a cunning and dangerous man who is too much like himself. He tells Brutus in Act II, Scene 1:
I think it is not meet
Mark Antony, so well beloved of Caesar,
Should outlive Caesar. We shall find of him
A shrewd contriver. And you know his means,
If he improve them, may well stretch so far
As to annoy us all; which to prevent,
Let Antony and Caesar fall together.
And when Brutus gives Antony permission to speak at Caesar's funeral, Cassius is horrified. He says:
You know not what you do. Do not consent
That Antony speak in his funeral.
Know you how much the people may be moved
By that which he will utter?
But Brutus overrules his partner. Brutus has changed too because of the power vacuum and because of all the adulation he has been receiving from his co-conspirators. He seems to be turning into another Julius Caesar--but without Caesar's cunning, cruelty, and practical wisdom.
Antony shows how much he has changed when he delivers the funeral oration that changes the course of history, then defeats Brutus and Cassius on the battlefield at Philippi, forms a triumvirate with Octavius and Lepidus, and subsequently becomes co-ruler of the Roman world.