There are two marriage certificates for Arthur and Sarah in the Maine Archives.(Also as I looked closer to the records, Sarah's middle initial is E in all the records. Ancestry.com showed a J on it's first short version of the certificate but when you look at the original certificate it is an E.
FROM THE MAINE ARCHIVES Certificate Number: Bride Name: STEVENS SARAH E Bride Town/State: WIENNA, ME Groom Name: WELCH ARTHUR G Groom Town/State: VIENNA, ME Date of Marriage: Wednesday December 17, 1919
Certificate Number: Bride Name: WELCH SARAH E Bride Town/State: VIENNA, ME Groom Name: WELCH ARTHUR G Groom Town/State: VIENNA, ME Date of Marriage: Wednesday December 17, 1919
Same persons in each, I believe.
FROM ANCESTRY.COM In the 1705-1922 records Ancestry.com has a picture of the actual marriage certificate. It shows that Arthur Welch was having his 4th marriage and Sarah E Welch (it does also show Welch for her) was having her second marriage. What is very interesting is that where the Groom and Bride are asked if they are widowed or divorced, they state they are MARRIED. (There is a question mark placed beside these answers.) Is it possible that these two were actually remarrying after a short time apart? I have seen this happen with another couple who remarried after being divorced for only two months. Or they were considered married by Common Law Marriage if they had been living together for several years?
This would answer the question why all but one child has her name on their birth certificate.