The idea that there is a connection between your mind and your body and the health of your mind can affect the health of your body is not confined to modern New Age spiritualists. Quite a few novels written in the 19th century having people falling into a decline and dying of some unspecified illness in a romantic way after losing someone dear to them.

I think I have read studies that show that people who are depressed are more likely to get physical illnesses, or have accidents and the like, but I can't recall any details.

JA postulates a bit more complicated link between the two in S&S - because she is distraught over Willoughby, Marianne goes walking in the wet and doesn't change her stockings and generally does such a poor job of taking care of her health that she catches a fever and nearly dies.