"The woman was killed by a heavy stone."
I wonder if "by" or "with" would be correct.
Please give me a correct word.
In this case I would choose with as stones are generally small objects and only lethal when used as weapons.
The woman was killed with a heavy stone. With is used to indicate what was used. It refers to the object itself (in this case the stone).
A woman was murdered in the city. The woman was killed with a heavy stone.
However if we take the example of a very, very large stone (a boulder) - we can construct an example using by.
The woman was killed by a heavy boulder. In this instance, By is used to refer to the cause of the occurance (her death). It is not linked to another person's actions. It explains what killed the woman (the falling boulder) - not who killed the woman and what they used to kill her.
A woman was driving along one of the mountain roads when a large boulder fell onto her car. The woman was killed by a heavy boulder.
Saying that somebody is done with something, we imply that there is another person or other people involved in the action; saying that somebody is done by something, we imply that something caused that particular action to happen, whether or not there was somebody else involved:
The woman was killed by a heavy stone. [the stone might just have fallen off a cliff or something else by itself, or might as well have been pushed down off a cliff by somebody else, causing her death]
The woman was killed with a heavy stone. [the instrument that was used by somebody to kill her was a heavy stone; it wasn't an accident, it was a murder]