Green’s Dictionary of Slang

weather n.

In phrases

under the weather (adj.)

(US) drunk.

1971		E. Wilson Show Business Nobody Knows 182: Dr. Harry Martin [was] lying on the floor, quite ‘under the weather’.
2020		A. Trebek The Answer Is 42: [M]y dad had managed to consume a bottle of rye and greeted me at the train station a little under the weather.