As far as I am able to tell,
overkill was
first introduced as a term used in
nuclear weapons
strategy. Any
weapon of mass destruction, when
used on a
populated area (
heaven forbid) will
kill far
fewer people than it could!
The reason is simple: the amount of energy released is sufficient to vapourise (literally, unfortunately) a huge number of people. But there are not that many people in the blast radius. Hence overkill: the excess energy released in the region.
Yet another reason why nuclear weapons should never be used.