Explain the line, "l can not say this death will weigh very heavily upon my conscience".

This last line of the short story is spoken by Sherlock Holmes. He is explaining how he got the poisonous snake Dr. Grimesby Roylott was using as a murder weapon to turn on Roylott and bite him. Holmes says he hit the snake with his cane to arouse its anger so that it would attack the first person it saw. That person was Roylott. The snake poisoned him, and he died. Holmes calls himself "indirectly responsible" for Roylott's death.
However, when Holmes says the death won't weigh very heavily on his conscience, he means that Roylott is a murderer who got his just desserts. Roylott had already used the snake to murder his stepdaughter Julia, and was trying to do the same to Julia's twin sister, Helen, all so he could keep control of their money. It is fitting that the snake he used against others was the cause of his own demise.