mid-14c., "to speak as an infant speaks," frequentative of blabben, of echoic origin (cf. Old Norse blabbra, Danish blabbre "babble," German plappern "to babble"). Meaning "to talk excessively" is from late 14c. Related: Blabbered; blabbering.
mid-15c., apparently from Middle English noun blabbe "one who does not control his tongue" (late 13c.), probably echoic. Related: Blabbed; blabbing. The exact relationship between the blabs and blabber is difficult to determine. The noun was "[e]xceedingly common in 16th and 17th c.; unusual in literature since c 1750" [OED].