Etymologists are at a loss to explain the origins of the word 'witch'. Old English 'wicce' is thought to originally mean 'female magician' or 'sorceress'. If 'wicce' is a female sorcerer, what is a male one called, you may ask. Well, such a person is called a 'wicca'. Both originate from the verb 'wiccian', wth the meaning of 'to practice witchcraft'.
The Dutch have a proverb that says na veel wikken en wegen, that means something like 'after much deliberation' or 'to weigh the pros and cons'. The word wikken is thought to be related to wichelen ('dowsing') and wichelroede ('dowsing rod'). These words are supposedly connected to the Old English wigle 'divination'. But we run again into problems here, because the true origin of these words are also uncertain.
But the Dutch verb wikken is also reminiscent of wiegen ('to cradle'). Those words are connected to English 'wiggle', meaning 'to rock' or 'to move from side to side'.
If one can imagine a witch as being a 'wise woman' who dabbled in herbal medicine, we can argue that she had to weigh her ingredients or weigh the pros and cons of which medicine would help the patient. But these 'wise women' also served as midwives, which could explain the word 'wiggle'. So, would it be possible that both the words 'witch', 'weighing' and 'wiggling' can be traced back to the same source?