To my (vague) knowledge, it is an word coined in romanticism to replace the French-rooted word Nostalgie, Schwermut was coined for Melancholie. The movement was fairly nationalistic and was unhappy with the dominance of French in high culture at that time. So they went ahead and coined "German" words were ones with French (or Latin) roots were used.

But please check/correct me on that, my memory might be betraying me here. Not even sure about the source...