Where does “fairylet” come from?

fairylet (English) comes from English Fairy, from Middle English faierie, from Old French faerie, from Old French fae, from Latin fāta, from Latin fātum, from Latin fātus, from Latin for — to speak, to be talking.

Ancestry of “fairylet”, step by step

fairylet traces back through two separate lines of ancestry.

via English Fairy

StepLanguageWordMeaning
1EnglishFairyA mythical being of human form with magical powers, known in many sizes and descriptions, although typically depicted as a small sprite with gauze-like wings, especially one that is female. Fairies are revered in some modern forms of paganism
2Middle EnglishfaierieThe land or domain in which magical or mythological creatures live; the Otherworld
3Old Frenchfaeriethe sphere or realm of enchantment, magic or...
4Old Frenchfae
5LatinfātaFate; Moira; goddess who controls destiny; divine personification of fate
6Latinfātumdestiny, fate, lot
7Latinfātusspoken, said, told, foretold, related, predicted; having or had spoken, etc
8Latinfor"defective"; I speak, talk, say
9Proto-Italicfāōrspeak
10Proto-Indo-Europeanbʰéh₂tito speak, to be talking

via English let

StepLanguageWordMeaning
1EnglishletTo allow to, not to prevent; To leave; To allow...
2Middle Englishletento let
3Old Englishlǣtanto let; leave; to let go, leave; to allow, let...
4Proto-West Germaniclātanto let, to allow; to leave alone
5Proto-Germaniclētanąto let, to allow; to leave alone
6Proto-Indo-Europeanleh₁d-to be tired
Every word from Proto-Indo-European bʰéh₂ti