What is the central idea of this excerpt?
Antony will be friends with the conspirators if they tell him why they killed his beloved Caesar.
He says he will support them if they explain their actions. ("Friends am I with you all, and love you all, Upon this hope: that you shall give me reasons Why and wherein Caesar was dangerous.")
The first two lines ("Therefore I took your hands, but was indeed Swayed from the point by looking down on Caesar.") simply mean that Antony was overwhelmed with grief to see the dead body of Caesar.