As the only untapped source of info,I couldn't resist downloading the will.The handwriting is the usual difficult one,but sufficient to identify references to son Stephenson,grandson Charles,and granddaughters Alice and Jane.
The following is very tenuous but may just hang together.There are two marriages of a Jane Lawson in Whitby in the 1830s.One is given as of 1830,a non conformist wedding(Roman Catholic or other?,might explain the difficulty finding records?),for a Jane Lawson born 1809 to a Captain William Garbutt.I can identify a Jane Garbutt in the 1851 census in Whitby,as a married mariner's wife living alone.(There are Merchant Navy records for a William Garbutt,born 1831 in Whitby,who might be their son).Even more tenuous might be identifying this Jane as the one in 1861 as a lodger in a Stephenson household,given born 1806).I have not pursued the possible 1837 marriage,nor have I ,yet,looked for Charles.
Regards
Roger