I agree about the term 'wid' not to be trusted.
In 1871, my gt grandfather was living as 'wid' with a string of his children, while his 'wife' was living with another man and new baby, assuming his name. She then married him in 1873, but my gt grandfather didn't die until 1875!!! I cannot say that she was a bigomist, as I have never managed to find a marriage for her to my gt grandfather, but they did have 11 children between them, before she 'moved on' and had 4 more!!!