From by way equivalent to be- + way. Compare German wegen (“because of, by reason of”).
Perhaps from the phrase "by the way(side)", equivalent to by + way.
"beway." YourDictionary, n.d. Web. 17 August 2018. <http://www.yourdictionary.com/beway>.
beway. (n.d.). Retrieved August 17th, 2018, from http://www.yourdictionary.com/beway