Why do the conspirators only choose to harm Caesar?

The conspiritors choose only to harm Ceaser and not anthonhy because brutus told them not to Brutus says that anthony is just a limb of ceaser, without the rest of ceaser he is nothing.

The decision not to kill Antony was that of Brutus. since he is hailed as being "honourable" he didn't want their actions to seem bloody and baseless. According to him he was delivering Rome from an ambitious dictator and not engaging into a killing spree.