A. According to Zoicher Habris (19: 1), Ateres Paz (38), and others, it derives from the German – Yidish gefatter or gevatter, meaning “shushbin” (best man) or godfather.
Oitzer Habbris (12 n. 2) mentions that it alludes to the fellow in charge to buying the diapers, that are named in a dialect by that name. He also quotes that it an expression of honoring by the door (kvod – tihr) or entrance to the shul. Aruch Hashulchan (Y.D. 265) maintains that it it connotes the k'tores or an offer of incense, since bringing the child to his bris is akin to sacrificing an oblation of k'tores.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a