Superman's one weakness was invented for a microphone, and its name is a chain of three borrowings.
The first link is chemistry. Etymonline says the element krypton was named in 1898 by its discoverers, Sir William Ramsay and Morris W. Travers, from Greek kryptos, "hidden." The gas had gone unnoticed for a long time and was hard to isolate.
The second link is Superman's homeland. Wikipedia's Krypton page says the planet, created by Jerry Siegel and Joe Shuster, "was named after the chemical element." The Krypton page adds that in the radio series the planet was a Counter-Earth on the far side of the Sun, which fits the Greek root, though it does not say that was the creators' intent.
The third link is the rock. Wikipedia says kryptonite was officially introduced in the radio serial The Adventures of Superman, in "The Meteor from Krypton," on June 3, 1943. Siegel had written an unpublished 1940 story with a prototype, "The K-Metal from Krypton," which was rejected. The comics followed in November 1949 in Superman #61.
Merriam-Webster notes that the earliest spoken use is in an Oxford English Dictionary transcript of that 1943 broadcast, followed by a 1945 newspaper mention and written comic-book use from 1949. Etymonline dates the word to 1943 and says it may combine "krypton" with "meteorite," though it calls the origin uncertain.
A popular story says the writers invented it so voice actor Bud Collyer could take time off. Wikipedia calls this apocryphal. Historian Michael J. Hayde disputes it, arguing that any vacation benefit came later and was incidental, and Wikipedia notes Superman is never exposed to kryptonite in that first episode.
The word then escaped the comics. Merriam-Webster cites a 1965 Shreveport Times baseball example, a single that ended a pitcher's scoreless streak, as evidence the word had left Superman behind. That is how it now means any particular weakness.