I suspect Albert Jack - referred to in the answer above - is a founder member of CANOE...that's the Campaign to Ascribe Nautical Origins to Everything!
He also claims 'square meal' is from a centuries-old nautical tradition of serving sailors' food on a square wooden tray. It isn't and is recorded nowhere prior to its use by hoteliers in mid-19th century America. (Click
http://www.worldwidewords.org/qa/qa-squ3.htm "> here for the opinion of Michael Quinion, a
proper etymologist, on 'square meal'.)
The word 'weather' has been used to suggest both beneficial
and unfavourable conditions since, of course, it may be nice and it may be nasty. I suspect that, joined to the word 'under', the automatic feeling is that it is nasty. Hence, 'under the weather' probably just meant grey, cold, nasty and all the other words one attaches to feeling unwell.
Red Herrings and White Elephants is an entertaining read, but I'd advise anyone to treat it as just that!