Permit
late Middle English (originally in the sense ‘commit, hand over’): from Latin permittere, from per- ‘through’ + mittere ‘send, let go’.
wiktionary
From Middle English permitten, borrowed from Middle French permettre, from Latin permittō(“give up, allow”), from per(“through”) + mittō(“send”).
An irregular borrowing from Spanish palometa, probably from a Doric variant of Ancient Greek πηλαμύς(pēlamús, “young tuna”).
etymonline
permit (v.)
early 15c., permitten, transitive, "allow (something) to be done, suffer or allow to be," from Old French permetre and directly from Latin permittere "let pass, let go, let loose; give up, hand over; let, allow, grant, permit," from per "through" (from PIE root *per- (1) "forward," hence "through") + mittere "let go, send" (see mission). Meaning "grant liberty or leave" is from 16c. Related: Permitted; permitting.
permit (n.)
"written statement of permission or licence, written authority to do something," 1714, from permit (v.).