I was wondering what is the difference in the nuances / usage of 気に病む and 心配する ?
(E.g. If I want to tell my friend not to worry about a test (albeit an important test), is it more appropriate to use 気に病むな or 心配するな ?)
It's simply a difference of image just like "Don't worry" and "don't make yourself sick over it"
It depends on the level of anxiety of your friend (気に病むな being stronger)
心配しないでね is the common saying, trying to get them from not worrying about it. I dont recall anyone ever saying 気に病まないで to me.
I would avoid using 心配するな because it is the command to "Dont worry!" as in "Dont touch or ill call the teacher!" kinda thing.