Would Humoresque (Joan Crawford, John Garfield, Oscar Levant) be considered a weepie? How about Sincerely Yours with Liberace? Those are two I always instantly recall in this kind of context from afternoon movies on black-and-white TV. Other than those, I'd name the Douglas Sirk films, first and foremost Imitation of Life which I clearly remember first seeing at a drive-in with the family.