This looks to be the 1851 census entry mentioned by Billie.
HO107 2413 folio 281
Newburn Village Northumberland
William Healey 39 Northd, Newburn Head Married File cutter
Jane Healey 37 Northd, Benwell Wife Married
John Healey 18 Northd, Benwell Son File cutter
Richard Healey 14 Sheffield, Yorkshire, Son File cutter
Alice Healey 12 Sheffield, Yorkshire, Daughter
William Healey 9 Northd, Newburn Son
Ann Healey 6 Northd, Newburn Daughter
Elizabeth Healey 3 Northd, Newburn Daughter
If Ann Atkinson was the sister of Jane Atkinson it would not have been legal for William Hedley senior to have married his dead wife's sister. Does Newburn parish register have the burials of Jane Hedley and her sister Ann Atkinson?
If William Hedley senior - the father of 'Puffing Billy' died in 1843 he would have been at least 90 if he was born prior to 1753.
Since Hedley seems a reasonably common surname in Northumberland and William is a common forename how certain is it that the William who married Jane Atkinson is the same man who had a son William by Ann (if illegitimate it should state it in the baptismal register which would give the child as 'William Atkinson' not 'William Hedley') and then later married Elizabeth Fletcher?
WILLIAM HEDLEY
JANE ATKINSON
Marriage: 10 APR 1773 Newburn, Northumberland
JOSEPH HEDLEY
Christening: 19 SEP 1773 Newburn, Northumberland
Father: WILLIAM HEDLEY
Mother: JANE
WILLIAM HEDLEY OR ATKINSON
Christening: 25 JUL 1779 Newburn, Northumberland
Father: WILLIAM HEDLEY
Mother: ANN ATKINSON
An illegitimate child had no claim on his father and could not inherit unless specifically mentioned in his father's will or if an inheritance was settled on him by his father in his life time.
The illegitimate son William seems to have been better educated and possibly better provided for than the half brothers by his father's second marriage - unless he was in himself a completely self made man? What were the occupations of the sons by Wliiam Hedley and Elizabeth Fletcher - were they similarly provided for?
Did William Hedley senior leave a will?
Regards
Valda