As fasting is so recently on our minds, when we received this question our inquiring mind wanted to know.
The word “fast” is interesting. It can also mean moving quickly or even not moving at all (fixed in place)!
Incidentally, when a word has two diametrically opposed meanings, the two word/meanings are called “auto-antonyms” or “contranyms.” We see such a word in Tanakh frequently: “cleave.” But again we have digressed from the question at hand.
The origin of the word “fast” is Germanic: fastuz, which meant “firm.” The word “fasten” also comes from it. As the word entered Old English (fæst), it meant “firmly fixed.” Think of color-fast or fast asleep. (The speedy sense came around the 1550s in the form of a verb which included the sense of determination and diligence.)
According to sources, the meaning of abstinence from food appeared around the 8th century, still in Old English (fæston), which seems to have developed parallel to the Gothic fastan (to keep, observe, which is much like our לשמור) and it was based in religion. (You knew I’d get around to religion!) The sense then was holding fast to a commitment, such as during Lent in the Christian tradition. Thus a verb was born of an adverb - holding fast became fasting.
Prior predecessor words may be found in Old Norse fastr, Old Frisian fest, and Dutch vast. There may have been many more permutations in the word’s history. There is also of course “fast living” from around 1745, and clocks were first said to run “fast” around 1840.
While we are fasting, however, the clocks seem to run slowly.