http://www.stormcam.org/scientific-weather/
Is there any scientific basis for the expression “under the weather”?
Some scientists believe that the weather affects humans much more than we realise in much the same way as it does animals. We already know about S.A.D. ( Seasonal affected disorder) which makes a sufferer feel depressed when not receiving enough sunlight which helps the body to produce vitamin D. Symptoms include lethargy , lack of appetite and generally feeling low and disinterested. Some people are particularly susceptible to magnetism and static caused by storms and suffer from a wide range of symptoms such as feeling nervous and jumpy before a storm and headaches and nausea.
This expression has been around for a number of years so I imagine that because people lived closer to nature years ago they had a greater understanding of this phenomenon and that’s probably where the saying emerged.
Oregon Scientific Wireless Weather Station