I'm writing an essay for English on Shakespeare's Juluis Caesar. In act III scene 2, Antony addresses Caesar's body as the noblest man. Later,...

Antony does not seem to have changed his mind when he speaks of Brutus as the noblest Roman of them all. It is actually in Act 3, Scene 1 that he addresses Caesar's body in a marvelous soliloquy. He says to the dead Caesar:

Thou art the ruins of the noblest man
That ever lived in the tide of times.

Caesar is, according to Antony, the noblest man that ever lived anywhere in the world. When he finds himself victorious at the battle of Philippi and is viewing Brutus' dead body, he says to Octavius:

This was the noblest Roman of them all.
All the conspirators, save only he,
Did that they did in envy of great Caesar;
He only, in a general honest thought
And common good to all, made one of them.

In other words, Brutus is only relatively the noblest Roman. He is the noblest of all the conspirators who assassinated Caesar. On the other hand, Julius Caesar was, in Antony's view, supremely noble. He was the noblest man who had ever lived at any time in history and at any place in the world. 

It does not appear that Antony has changed his mind. When he and Octavius meet with Brutus and Cassius in a parley just before the battle at Philippi, Antony insults them both, but he is speaking directly to Brutus, who has just insulted him in referring to the Hybla bees:

For you have stol'n their buzzing, Antony,
And very wisely threat before you sting.

Antony replies:

Villains! You did not so when your vile daggers
Hack'd one another in the sides of Caesar.
You show'd your teeth like apes, and fawn'd like hounds,
And bow'd like bondmen, kissing Caesar's feet;
Whilst damned Casca, like a cur, behind
Struck Caesar on the neck. O you flatterers!

He is calling Brutus as well as Cassius "villains" and "flatterers." He could not be more insulting. He could hardly think of Brutus as being on the same level as Julius Caesar if he talks to him like this. Brutus had been hoping that their differences could be settled without bloodshed, but after this the parley breaks up and the fighting commences.

So when Brutus is lying dead and Antony calls him "the noblest Roman of them all," he obviously means that Brutus was the noblest Roman of all the conspirators, which is certainly true. Brutus is far nobler than his fellow-general Cassius, who is money-hungry, self-seeking and dishonest. Shakespeare intentionally contrasts these two characters because they are so important in his interpretation of history. Perhaps Brutus was too noble for the role in history that he was called upon to play.