Explanation:

- Wriggle: Correctly spelled. It means to twist and turn with quick movements.

- Wreathe: Correctly spelled. It means to surround or encircle in the form of a wreath or to twist into a circular shape.

- Weggle: Incorrectly spelled. This word should be "Wiggle," which means to move up and down or from side to side with small rapid movements.

- Wreak: Correctly spelled. It means to cause or inflict something, especially damage or harm.

Weggle is the incorrectly spelled word.