Coincido con todos en que significa sentirse mal física, moralmente o ambas cosas a la vez, pero me parece que dicho en forma negativa queda mejor en español.

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Note added at 15 hrs (2019-04-20 22:01:07 GMT)
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Parece que en origen la expresión se refería al malestar físico y se amplió más tarde al estado de ánimo. Copio esta referencia:

Origin Of ‘Under The 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 recovery, under the deck and away from the weather.”
According to another source, a book called Salty Dog Talk: The Nautical Origins of Everyday Expressions, by Bill Beavis (Author) and Micahel Howorth (Author), it says that this phrase originally meant to feel seasick, or to be affected by bad weather (while out at sea, I assume). It also 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.”
https://knowyourphrase.com/under-the-weather