I assume that Wheldon was a name he assumed at a later date, as there does
not seem to have been any birth registered with that name in England or
Wales in 1844.
Of the 108 births of John WILLIAMS registered in England and Wales in the
months of April May and June 1844 only 59 were in Wales.
There were 43 occurrences in March quarter 1865 to June quarter 1870 where a
John WILLIAMS appeared on the same page of a register of marriages as a Mary
JONES, all but about 4 in Wales.
If Wheldon was his mother's maiden name, which he appropriated to use to
distinguish him other people called John WILLIAMS, it is worth looking to
see where than name was common.
There were only two occurrences of marriages in the period from start of
civil registration in 1837 and June quarter of 1845 of a WHELDON and a
WILLIAMS occurring on the same page of marriage index, both in Carnarvon
district (modern Caernarfon), North Wales. However in both cases both were
men, among the 8 names per page of the index.
WHELDON was not a Welsh name. It seems to have been concentrated in
North-East England in the 1840s.
This much from
http://www.freebmd.org.uk/
From Ancestry.co.uk there seems to have been only one Wheldon family
in
Wales in 1841census, in Mold in Flintshire.
Familysearch Batch number C056651 in the IGI shows the baptisms of this
family in Mold parish church 1818 to 1834. The oldest girl in the family.
Elizabeth bap 1818, is not with the family in 1841 census. She may have died
or married. There was an Elizabeth WHELDON married in Liverpool in 1839.
None of the men's names is WILLIAMS.
http://www.ukbmd.org.uk/genuki/reg/districts/holywell.html shows that Mold
was in Holywell registration district. There were three John WILLIAMS
births in Holywell district in June quarter 1844. One had the middle name
Cadwalader.
One reason for use of a double surname could have been an illegitimate
birth to a WILLIAMS where the acknowledged father was a WHELDON. If that was
the case in Wales, not many places to look.
One of the most important clues would be John's occupation when he came to
Pennsylvania. If he was a coal miner he probably came from a coal mining
area. If a slate quarryman, probably from a slate district.
There were a number of Elizabeth Jane WILLIAMS births in Wales in 1869.
Best wishes with your researches.
Jeff