i rest my case http://www.phrases.org.uk/bulletin_board/18/messages/735.html: It's of legal origin, with "case" meaning argument or claim - as in the case against legalising soft drugs, for example. To this day in British courtrooms (and probably elsewhere in the English-speaking world), when the Prosecution (or the Defence) has finished calling all its witnesses and introducing into evidence all the items that it feels beneficial, its lawyer will tell the court that "the Prosecution rests". Of course the right of cross-examination of any witnesses introduced by the other side still remains.
: To say "I rest my case" means therefore that, as far as you are concerned, you've done more than enough to prove your point, and need say no more. It's often used in an ironic manner, to highlight when someone inadvertently says something that supports the claim you are making, as in the follwing example:-
: John: "You know your problem, Bill? You're far too quick to descend to insulting people who disagree with you."
: Bill: "Don't be ridiculous! That's the sort of thing only a complete idiot would say."
: John: "I rest my case..."
Actually, the example given there is the common usage rather than the original. The common usage is "what you've just said proves my point" rather than the less definite original usage.
The legal origin is that each side to a dispute is given a certain opportunity to present their version of the facts, whether by calling witnesses, or by reference to documents etc - when the evidence has been concluded that is when each side then makes legal argument to the judge/jury in turn. When the turn is finished the advocate is said to "rest" their case. The opening party rests their case first, which is why the opponent can submit that there is "no case to answer" at that point. After both sides have rested, then the judge rules (or rules after a jury has delivered a verdict) and then the parties can again take up their cases to argue about the responsibility for legal costs of the action. It is probably because the parties once again may need to argue after the delivery of the judgment that the cases are said to "rest" as in pause, rather than some more conclusive word.
I have made out my argument, I rest my case.
BTW on that line - a "briefcase" was a case used to carry briefs to court - briefs being the summary of the instructions and evidence of one side.