Norma June Mayfair is the mother of Maw Maw. She made an appearance in season 3, during the mothers day episode. Barney and Burt decide to drive up to Maw Maw's childhood home to take pictures, and hopefully jog Maw Maw's memory. When they arrive, an extremely old woman (Barney referred to her as the "little guy from Lord of the Rings" - being Gollum) and the woman turns out to be Norma June Mayfair, the mother of Maw Maw. She is 104 years old, and believes she was dead for 20 years, and was waiting for angels to take her to heaven (although she was very much alive). She greets Burt and Barney with a shotgun, that is not loaded. She was also portrayed by Chloris Leachman, who is the actress who plays Maw Maw.
Norma June Mayfair and Maw Maw hadn't seen each other in 70 years. They had a falling out when Maw Maw was younger. What happened was that Norma June sent Maw Maw out for heating oil, and she got "flim flamed" and the man never delivered the heating oil. Maw Maw later went out to the movies, but since Maw Maw gave her money to the oil man, she used her "feminine wiles" to get in to the movie for free. When Maw Maw got home, and realized that she was, as she put it "Flim Flamed" and her mother accused her of not getting oil, and using her money to go to the movies. When Maw Maw and Norma June see each other at the house, they immediately start fighting and Maw Maw lunges at her mother. They fight until Virginia and Burt broke up the fight. Then, Maw Maw pays her mother to get her off her back (25 cents) they hug, and make up. Then, Norma June goes to the bathroom and farts the whole way there. She later exclaims very loudly that Sebrina and Virginia hears her outside "FRUITCAKE, WHEN THE HELL DID I EAT FRUITCAKE!". Unfortunately, Barney goes to the bathroom later to check one her (as she has been in there presumably more than an hour) and finds her dead. Barney tells Burt and they call an ambulance. They don't tell anyone that she died, and didn't want Maw Maw to know, so when people ask where she is, they say that she left, and later told Virginia.
Her only appearance was in the Mother's day episode in season 3. Remarkably, this means that she was 104 and alive to meet her Great Great Great Granddaughter, Hope Chance.