"edge, rim," 1459, from M.Fr. verge "rod or wand of office," hence "scope, territory dominated," from L. virga "shoot, rod stick," of unknown origin. Earliest attested sense in Eng. is now-obsolete meaning "male member, penis" (c.1400). Modern sense is from the notion of within the verge (1509, also as Anglo-Fr. dedeinz la verge), i.e. "subject to the Lord High Steward's authority" (as symbolized by the rod of office), originally a 12-mile radius round the king's court. Sense shifted to "the outermost edge of an expanse or area." Meaning "point at which something happens" (as in on the verge of) is first attested 1602. "A very curious sense development." [Weekley]
"tend, incline," 1610, from L. vergere "to bend, turn, tend toward, incline," from PIE *werg- "to turn," from base *wer- "to turn, bend" (see versus). Much influenced by verge (n.) in its verbal form meaning "to be adjacent to" (1787).