late 13c., "to give an edge to" (implied in past participle egged), from edge (n.). Intransitive meaning "to move edgeways (with the edge toward the spectator), advance slowly" is from 1620s, originally nautical. Meaning "to defeat by a narrow margin" is from 1953. The meaning "urge on, incite" (16c.) often must be a mistake for egg (v.). Related: Edger.
<a href="https://www.etymonline.com/word/edged">Etymology of edged by etymonline</a>
Harper, D. (n.d.). Etymology of edged. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/edged