In the Ch. 29 vocabulary list in Wheelock, ‘fairy’ is listed as a derivative of Lat. fatum. I hadn’t known this, so I decided to look it up quickly in the OED. The etymology for ‘fairy’ is: a. OF. faerie, faierie (mod.F. féerie), f. OF. fae (mod.F. fée) FAY n.2.
And ‘fay’ is derived from fatum as follows: ad. OF. fae, faie (Fr. fée) = Pr. and Pg. fada, Sp. hada, It. fata:–Com. Rom. fata fem. sing., f. L. fata the Fates, pl. of fatum FATE.
One can perhaps see how ‘fairy’ came from fatum in definition A.4.a.: ‘One of a class of supernatural beings of diminutive size, in popular belief supposed to possess magical powers and to have great influence for good or evil over the affairs of man.’