Idiomatic, Usually, With of A weak member of a peer group, especially the weakest.
The former openly likens Cuba to Turkey, saying that the island is the "sick man" of the West;1854, H.B. Stowe, “America's Ambition and Europe's Dilemma”, in The Living Age, volume 42, page 245:
The House of Lords has now come to be pretty generally looked upon as the "Sick Man" of the English Constitution.1896, Jesse Macy, The English constitution: a commentary on its nature and growth, page 54:
2 more examples
He told how in an economic sense we were one of the Sick Men of the World our industry dilapidated rundown and was not being renewed1942 May 19, “The Home Front”, in Los Angeles Times:
For Asia as a whole, that target was just about achieved, even when including India and Indonesia, often regarded as the "sick men" of the continent.1970 January 19, “A Decade of Disappointment for Asia”, in New York Times: