The old saying, "I can feel it in my bones", refers to how people with arthritic joints or aches from old broken bones seemed to ache in damper colder weather.
Most medical research claims no real proof that people can essentially 'feel' a storm is on the way. There are other researchers that claims that barometric pressure and humidity changes can cause a rise in pain from various long term illnesses like rheumatoid arthritis, gout, osteoarthritis and fibromyalgia. The claim goes on to claim it can make headaches worse, worsen back pain and cause many other body aches.
Hippocrates, the father of medicine, noticed that some illnesses seem to be seasonal. In traditional Chinese medicine, there is a cycle and that can have an impact on various ailments. This shows the Chinese saw different times of the year bring out more symptoms in certain people.
The connection from belief to practical medicine isn't too far to leap in this case. Pain is a very subjective thing and maybe your uncle Bob can feel it in his old broken toe when it's going to rain.