In Act 1, Scene 2 when Cassius is speaking to Brutus, Cassius describes two instances in which Caesar showed weakness and needed help. At one time Caesar challenged Cassius to swim across the Tiber River with him when the weather was bad and the river was turbulent. Cassius immediately dove into the water and Caesar followed. But Caesar became exhausted and cried:
"Help me, Cassius, or I sink."
Cassius tells Brutus how he rescued Caesar from the waves. The point of this anecdote is to prove that Caesar is not the strong man he pretends to be. It is true that Caesar was sickly in his youth. He fought against it all his life, forcing himself to endure all kinds of hardships. He had infirmities such as epilepsy ("the falling sickness") but he compensated for his weak constitution with his strong will. His weaknesses were what motivated him to become strong--but this is true of many people. Theodore Roosevelt is a good example.
Cassius cites a second instance of how he helped Caesar when he was weak and in need of support. Presumably Cassius stayed with Caesar until he recovered from a serious illness.
He had a fever when he was in Spain,
And when the fit was on him, I did mark
How he did shake. 'Tis true, this god did shake;
His coward lips did from their color fly,
And that same eye whose bend doth awe the world
Did lose his luster. I did hear him groan.
Ay, and that tongue of his that bade the Romans
Mark him and write his speeches in their books,
Alas, it cried, “Give me some drink, Titinius,”
As a sick girl.
Cassius is not being entirely logical. The fact that Caesar has physical problems does not mean that he is not mentally competent to be the monarch he aspires to be. Caesar has proved that he was capable of being a great general. His men revered him. He enlarged the Roman empire and suffered the worst kinds of pain and privation for years during his many successful campaigns. Cassius is speaking out of hatred, fear, and envy. By implication, Cassius is as good a man as Caesar and fully as capable of wielding Caesar's power. Brutus does not hold the same high opinion of Cassius as Cassius holds of himself. When they are having their violent argument in Brutus' tent in Act 4, they have the following exchange:
When Caesar lived, he durst not thus have moved me.
Peace, peace! You durst not so have tempted him.
I durst not?
What, durst not tempt him?
For your life you durst not.