I think it goes back to Fannie Farmer in 1896, who wrote the first major and comprehensive cookbook in English that used any kind of standard measurements. European cookbooks mostly used vague instructions without any standardized weights or numbers before that. At this point in the industrialized world standardized cup measures were relatively cheap and available. Scales were relatively bulky, expensive, and inaccurate in 1896. So the whole tradition got started, and most of the major cookbooks owed something to Fannie Farmer. Cookbooks that used standardized weights probably got started in other countries much later, when scales were becoming commonplace.