Where does the phrase "fit to be tied" come from? Has its meaning become diluted?

While looking into an answer for "Sick and tied" and "sick and tired", I stumbled across the idiom fit to be tied which according to thefreedictionary means angry and agitated. (As if needing to be restrained.)

A second search turned up that this refers to the practice of bounding uncontrollable, dangerous people into strait-jackets. How did we make the leap from crazy and uncontrollable to the general usage today of ticked off? Or is my understanding of general usage today incorrect? Is it common for these phrases to become so watered-down over time?

You are correct about the current usage. You would not use it to refer to a mental patient in the technical sense, but apparently it was at one time acceptable to do so. I would have thought that the idiom started life in the "angry and agitated" sense, but there is one old (1804) citation that I found via an ngrams search which uses the second sense, apparently without irony. I do not know when the newer sense of the phrase took over, but it was certainly in use about 100 years after that first example.

"Mad" itself seems to have followed the same path. The earliest citations in the OED refer to the "mental disease" aspect, and the "uncontrollable rage" meaning comes later, followed by the colloquial sense of "angry".

It seems to be a common pattern, that a technical phrase for a mental condition gets borrowed for colloquial use and then falls out of usage in its original sense to avoid offense. "Retarded" is another example: the use of the word as an insult and "synonym" for "unintelligent" put it onto the Euphemism treadmill.

This phrase was used frequently by my mother and my aunt. My mother was born in 1909, my aunt in 1915. They grew up in western Pennsylvania in a conservative home where no one used strong language. They used it to mean being very agitated or annoyed by circumstances caused by thoughtless or unpredictable behavior. For instance, "I was fit to be tied when the boys ate all the cake before the party". Or, "I was fit to be tied when the water pipe burst just after the plumber left". There was never the connotation of mental illness or uncontrollable emotion, rather it referred to justified anger.

That's funny: I, too, am a son of parents whose roots go back seven generations in Pennsylvania, and that is where I picked up the expression, "fit to be tied."

I always had the sense that it meant, "having such a fit, that one's arms might have flailed around, so that it might have crossed one's mind to be tied for that time, to prevent damage to nearby knick-nacks, or to prevent one from throwing something." It conveyed a sense of a temporary fit, and maybe even a serious one, but not quite the same as "anger, or rage, or wrath" per se, that would connote a long term bitterness or hardness of heart. Somehow, I always got the impression that the expression was used when someone became a bit more than just annoyed, like after a prank was pulled on them.

Where I live, "fit to be tied" describes a state of extreme puzzlement and possibly irritation. There isn't necessarily any anger, but there could be. (I live in Saskatchewan, Canada.)