Green’s Dictionary of Slang

(US campus) used of someone seen as acting like a big brother or sister.

1985		Eble Campus Sl. Oct. 1: Beav & Wally – names that males call each other in jest, referring to the little brother/ big brother.
1996		Eble Sl. and Sociability 92: Leave It To Beaver, which originally aired from 1957 to 1963, in the late 1980s was still being tapped for Beav and Wally, names that college males called each other in jest when caught acting in the role of either a little brother or a big brother.