It may also be important to note that those contents of the will may not have been entirely truthful, just a mechanism that Antony used to get the people to support his cause. We are supposed to believe that after Caesar's death, Antony raced to JC's house, quickly explained to Calpurnia that JC is dead, quickly found his will, and made it back to the senate in time to give his speech. Further, look at Antony's lines when he comes down from the pulpit with the will. He asks the crowd to stand farther off - not to crowd him. It's possible that Antony made up some of the legacies in that will.
The contents of Caesar's will is Antony's key in "turning" the people against the conspirators. (I'll give you the contents in a minute.) The conspirators disliked and envied Caesar, for a variety of reasons: Caesar had numerous affairs with powerful men's wives, he was loved by the common people, and Caesar loved power...(which would dissolve the triumvirate). In essence, the conspirators started a smear campaign against Caesar. He was too old, infirm (epilepsy), proud, couldn't hear, etc...how could he possibly rule? Antony's skillful oration uses plays on words and repetition to sway the fickle crowd into a raging riot. Could a man who left every Roman citizen (not everyone) seventy-five drachmas, walks, arbors and new-planted orchards be as horrible as the conspirators were making him out to be? After seeing Caesar's body and hearing the will, the crowd pursues the conspirators. The conspirators flee Rome.
The content of his will was completely unrelated to what was read by Marc Antony. Caesar's will left pretty much everything to Augustus (at that time Octavian), but Marc Antony made up information in order to make it sound like Caesar was a kind and benevolent person, not just some guy who ripped off Marius and Sulla
Antony was a supporter of Caesar and hated Brutus and Cassius for murdering him. So, as well as as announcing that Octavion would be made his only legal hier, he wanted the plebs to know that he was leaving them 300,000 sesterces each. This, Antony knew, would infuriate the people toward his murder so much that it would force Brutus and Cassius to leave.