Avid readers of the Harry Potter stories will know that Ron Weasley had a tiny owl, which to his disgust his sister Ginny named Pigwidgeon. It was appropriate because the word has often meant a small or insignificant person or thing. It has also been used for a stupid or contemptible person:
“Think?” I queried, “do I ever really think? Is there anything inside my head but cotton-wool? How can I call myself a Thinker? What am I anyhow?” I pursued the sad inquiry: “A noodle, a pigwidgeon, a ninnyhammer, a bubble on the wave, a leaf in the wind, Madame!”
More Trivia, by Logan Pearsall Smith, 1921.
The original sense, however, was of a species of fairy, dwarf, imp or elf. These were also small, though lacking the deep cunning and capriciousness of many other little people. They were often considered to be more mischievous than nasty:
In Malvina, side by side with much that is commendable, there appears to have existed a most reprehensible spirit of mischief, displaying itself in pranks that, excusable, or at all events understandable, in, say, a pixy or a pigwidgeon, strike one as altogether unworthy of a well-principled White Lady, posing as the friend and benefactress of mankind.
Malvina of Brittany, by Jerome K. Jerome, 1916.
The experts guess that the first part of the word may be connected with pug, another old name for a fairy, which may be a variation on puck. The second part was once wiggen, an unknown word that was said with a hard g; later it shifted to widgeon with a soft j sound because in the seventeenth century the duck that went by that name was a byword for being stupid.