Hi Robin
Re the William James PAY born in Deal in Kent.
Don't believe this can be your William J.
In Rosie99's post #22, she has followed him up for you.
"The William James Pay who you have born in Deal Kent
Baptised 23 Oct 1833 at Deal parents James & Mary
In 1851 he is living with his parents and his occupation is twine spinner.
In 1861 - RG9/ Piece 482 Folio 42 page 40 living at Chatham age 28 occ Rope Maker with wife Hester age 27 born Suffolk"
Rosie goes on to say in #23 that this William James is not with 'wife' Hester in the 1871, but given the change in occupation, it seems unlikely that he is the barman (and associated occupations) on William Arthur (and the other children)'s birth certificates.
As I said in a recent post, the death in 1874 cannot be him as it is a child. A death could also be registered as simply William (no middle name mentioned), so difficult to track down with certainty.
Ada Emily Pay and her family George Pay and Mary (Smith) Pay
Rosie99 in #19 has found Ada with her father George and mother Mary (Smith) Pay in the 1851, with siblings George and Ellen (and presumably mother Mary's nephew Edward Smith). There was another daughter Emily, who possibly died and I have not as yet found her death ref.
I agree that Ada is a servant in the 1861 in the other census Rosie quotes.
This makes it clear that Ada is in fact a PAY, and casts doubt on whether William James was also a PAY.
Rosie also found in reply #26 a further link between Ada and her children and the Pay family in that in the 1854 at the baptism of Ada's sister Ellen, the Pay family are at 2 Browns Court in Marylebone. This is the address for Ada and her own family in the 1881 where she's shown with the children but widowed.
going back to the history of George Pay
I have tracked down Ada's father George Pay, who comes from a small place in Sussex called Funtington. He is (I believe) the son of Edward Pay and Amelia (Trusler) Pay, and was born c 1814-17 in Funtington.
He appears in two censuses, the 1841 and the 1851, and there is also a baptism in Funtington in Dec 1814.
He marries Mary Smith in 1836 in St Pancras Parish Chapel (both sign their name).
Whilst Mary (Smith) Pay appears in the 1861 census with her 'nephew' Edward/Edwin Smith, shown as married, occupation 'coachman's wife', I cannot as yet see George Pay who is presumably working away from home. He does not appear to be with any of his siblings.
I can at present not see either George Pay or Mary (Smith) Pay in later censuses.
Next steps if you want to take them...
Rosie has asked if you have the birth certificates for any of the Maling children which would give addresses.
I have been looking for 'barmen' in the 1871 census called William James or William, in the rough locality of Ada's address at the time, or in Marylebone. This produces a number of possibilities but all would need tracking down in the 1861 and after 1871 and is a long task as well as highly speculative.
Have you taken a DNA test? This is likely to be the only way you will find out who the William James could be, the father of your ancestor William Arthur - because it seems very likely that the PAY surname came from Ada.