The source of this expression, which means delighted, is a hook-nosed puppet named Punch. He quarreled with his shrewish wife, Judy, in "Punch and Judy" shows beginning in the early 17th century. The name "Punch" was derived from "Polichinello," a character in Italian puppet plays.
The original saying was "proud as Punch," and it had a negative connotation because Punch is vain, pompous, and enormously pleased with his victories over his spouse.
In 1841, Punch became the title of a humor magazine that grew to be very popular. But the origin of that name lies in the Indian "panca," a party beverage often served from a bowl.
SOURCES: 'The Barnhart Dictionary of Etymology,' by Robert Barnhart; 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson; 'Clichés,' by Betty Kirkpatrick; 'A Dictionary of Clichés'; Webster's New World College Dictionary (Fourth Ed.).