The Wolff family of Paramus, N.J., was eyeing the gathering clouds and debating whether to cancel a planned park trip when 6-year-old Leora piped up with an idea: "Let's call Grandma. Her knees always know when it's going to rain!"

Leora's grandmother, Esther Polatsek, says she started being sensitive to the weather in her 20s, when a fracture in her foot would ache whenever a snowstorm approached. Now 66 and plagued by rheumatoid arthritis, Mrs. Polatsek says she suffers flare-ups whenever the weather is about...