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Phrases and Idioms - The Meanings and Origins For Popular Idioms and Phrases
Feeling sick; ill. It can also mean that a person is feeling sad or depressed.
* Elise just got back from her vacation in Florida, but sadly, she returned feeling a bit under the weather because she had a sore throat, a runny nose, and a fever.
Note: A phrase's origins are unclear a lot of the time. Hence, while this doesn't go for every phrase, the origins you see listed are the plausible theories floating around for how or where an idiom may have come from. The quotes which have the phrase in them are the oldest written forms of the phrase I could find, but keep in mind that older recordings might exist and perhaps I overlooked them.

Also, remember that just because you see a saying in an old book or newspaper, let's say from the year 1893, it does not mean the saying originates from that source. In all likelihood, if an expression is already in use in a book or newspaper, then it's probably older already commonly known. Nevertheless, these old quotes serve as a way to show the reader how far back in history some of these sayings go.
The sun and rain! Weather!
This phrase possibly has nautical or seafaring origins. Commenting on the origins
of this expression, a website called The Phrase Finder mentions that in the old days,
when a sailor was feeling seasick, "he was sent down below to help his reocvery,
under the deck and away from the weather."

According to another source, a book called Salty Dog Talk: The Natuical Origins of Everyday Expressions, by Bill Beavis (Author) and Micahel Howorth (Author), it says the following regarding this phrase: "To feel ill. Originally it meant to feel seasick or to be adversely affected by bad weather." It goes on to say: "The term is correctly 'under the weather bow' which is a gloomy prospect; the weather bow is the side upon which all the rotten weather is blowing."

The earliest recording that I could find of the idiom is from the newspaper Jeffersonville Daily Evening News, 1835, and it says:

"'I own Jessica is somewhat under the weather to-day, figuratively and literally,' said the gentleman,
amusedly, giving a glance at the lady over in the corner."

Reference: The Phrase Finder, Salty Dog Talk: The Natuical Origins of Everyday Expressions, by Bill Beavis (Author) and Micahel Howorth (Author)
Know Your Phrase - Popular Idioms and the Meanings for Common Sayings > U-Letter Expressions