This is a fascinating Welsh folk song since it was seemingly handed down in a single family from Cei Newydd in Ceredigion, with the warning that it should not be sung in public. It's doubtful if such Marian verses could have been composed in Wales during the non-conformist period and therefore it's believed that the words date back at least as far as the Reformation.
It came to wider notice from schoolteacher Myra Evans 1883-1972 (born Jane Elmira Rees) who got it from her mother, who in turn learnt it from her grandfather David Williams. Elmira Rees's father was a mariner, like many of the men in New Quay - you'll not find him in some of the census records since, presumably, he spent so much time at sea. I wonder if the absence of husbands from the household accounted for the longevity of such an "old-fashioned" and matriarchal song.
There's a recording by Elen Manahan Thomas on youtube but this version is from Siwsann George.