It didn't bring about modern literature. It supported the genres of horror and fantasy.

Weird Tales was part of the pulp magazine phenomena. The pulps were notable as purveyors of entertainment for the common person, not the reader of "literature." They also developed into tight niche markets, designated by their titles. My favorite actual mag showing this pigeonholing was Spicy Oriental Pirate Stories. They wouldn't even take spicy (sexy) pirate stories set in the Atlantic!

Now, in its genre, Weird Tales was extremely influential. It was pretty much the only place HPL sent any work, or Clark Ashton Smith published. Robert E. Howard published all over, because he wrote all kinds of genres, including boxing stories. While most of his Conan stories did appear in Weird Tales and were influential to the point that C. L. Moore's Jirel of Joiry was called "a gal Conan," much of the influence of Conan is from the 1960s forward by other writers than REH:

The character of Conan has proven durably popular, resulting in Conan stories by later writers such as Poul Anderson, Leonard Carpenter, Lin Carter, L. Sprague de Camp, Roland J. Green, John C. Hocking, Robert Jordan, Sean A. Moore, Björn Nyberg, Andrew J. Offutt, Steve Perry, John Maddox Roberts, Harry Turtledove, and Karl Edward Wagner. Some of these writers have finished incomplete Conan manuscripts by Howard. Others were created by rewriting Howard stories which originally featured entirely different characters from entirely different milieus. Most, however, are completely original works. In total, more than fifty novels and dozens of short stories featuring the Conan character have been written by authors other than Howard. (Wikipedia)

I don't think that even counts the comics.

So for horror, Weird Tales was extremely important: HPL is often considered the second great master of horror, following Poe and preceding King.

For heroic fantasy/swords & sorcery, they were very notable, though not top flight. As Michael Moorcock said of REH, he

"was never a commercially successful writer in his lifetime. His brash, hasty, careless style did not lend itself to the classier pulps. Most of his work appeared in the cheapest of them."

That's Weird Tales.

Lovecraft scholar S. T. Joshi wrote, in his biography H. P. Lovecraft: A Life, that "The bulk of Howard's fiction is subliterary hackwork that does not even begin to approach genuine literature" and "The simple fact is, however, that his views are not of any great substance or profundity and that Howard's style is crude, slip-shod, and unwieldy. It is all just pulp—although, perhaps, a somewhat superior grade of pulp than the average."

You might look into some of its competitors, like Astounding science Fiction, which later became Analog. Unknown, which pioneered urban fantasy. "The magazine is generally regarded as the finest fantasy fiction magazine ever published, despite the fact that it was not commercially successful, and in the opinion of science fiction historian Mike Ashley it was responsible for the creation of the modern fantasy publishing genre."

Source: H. P. Lovecraft: A Look Behind the Cthulhu Mythos by Lin Carter.