The earliest use of the term “weird fiction” I can find is in the Australian Journal, 1872, said of a ghostly oral tale of the outback…

Interestingly the headless horseman of British lore was here transformed by the Australians from a fearsome spectre into an aloof guardian, or so it might seem.

The term moves into literary use with The Library Table, 1878, used of Gaboriau-esque detective mysteries set in the dank and decaying pre-Haussmann city of Paris…

1879, from a survey of The Homes of America, said in passing of The Legend of Sleepy Hollow tales of Washington Irving…

In summer 1894 there appears a well-reviewed anthology of the “weirdest Oriental stories” … “weird literature of the East”, as retold by aficionado Lafcadio Hearn.

The genre is now well known if diffuse, and in 1892 the Mormon Young Woman’s Journal takes care to distinguish children’s fairy stories from “weird literature”.

The first journalistic use that can be found, by a book reviewer using it in the modern sense we would recognise today, is from 1894. From Philadelphia, Lippincott’s Monthly, November 1894, “Book Notes”. This credits Poe as the inventor, but also notes the German influence…

Evidently we are not talking here about folk tales, fairy stories, ghost stories, Oriental stories or early Parisian detectives. The fine evocation of atmosphere is a key element, and this implies a readership willing and able to savour it rather than rush ahead to the next penny-dreadful ‘shock’.

Can anyone beat 1894, with the term used in the modern sense?

There was probably then some throwback of the term, using to ‘net’ earlier fiction that might have once been classified differently. Here, for instance is “weird fiction” in popular newspaper use in February 1905 in Canada, by a literary critic remarking on an aspect of the famous Dr. Jekyll and Mr. Hyde (1886). The clever editor has run a suitable but unrelated cartoon next to the article.