Reference Librarian assisted; together we were not able to locate a hardcopy of Asbornsen's work (translated to English), specifically including 'Berte Tuppenhaug'.
I did find it on-line in Norwegian, as 'Berthe Tuppenhaugs fortellinger':http://runeberg.org/folkeven/018.html
The auto translator didn't work well on it, language is archaic. Another research site provided that: Berthe Tuppenhaug is an old women with speial talents to cure people with blessing and witchcraft. Mads Knai was her uncle & some of his happenings are described in Berthe Tuppenhaugs fortellinger. Tuppenhaug is the name of the cottar place where Berthe lived. Tuppen = the tip, Haug = hill.
Thought you might enjoy what I had found earlier about this fairy tale.