In act one, scene two, Caesar remarks that Cassius "has a lean and hungry look" and says also that "He thinks too much." The implication here is that Cassius is ambitious; he is "lean and hungry" like a wild animal looking for prey. Caesar is also suspicious of men, like Cassius, who think "too much," presumably because men who think "too much" are liable to plot and scheme, especially if they are "lean and hungry."
Antony, however, tries to reassure Caesar, saying that Cassius is "a noble Roman and well given," meaning that he is honorable, and has a good disposition.
Despite Antony's reassurances, Caesar is still wary of Cassius. He says that Cassius is too serious and that he doesn't love plays, listen to music, or smile as Antony does. Perhaps Caesar here is anxious that Cassius is unhappy, and unhappy men are, of course, more dangerous than happy men, especially when they are as clever as Cassius. Caesar also says that such men as Cassius "are very dangerous" as long as "they behold a greater than themselves." The implication here is that Cassius is, according to Caesar, someone who doesn't like to serve someone greater than himself.
In his speech later in the play, after Caesar has been murdered by Brutus, Cassius, and others, Antony repeatedly says to the gathered crowd that Brutus and Antony "are honorable men." He repeats this five times so that the phrase becomes laced with sarcasm. Antony thinks that the assassination of Caesar, and thus Cassius's part in it, was anything but honorable. At this point he likely regrets the reassurances he offered to Caesar earlier in the play.