I too have a William Burleigh/Burley who married a
Matilda Wilson, arriving in Canada 1834 shortly after
marriage in Fermanagh. When my William died in 1903,
one obit said he was 106, another said he was 103 but
1901 census in Canada said he was born in 1804.
Early records give his religion as Bible Christian,
later ones are Anglican.
Somehow our Williams must be connected given the
children's names of mine born in Canada:
James Nelson 1838; Margaret Jane 1840; Thomas Irvine
1843; Rebecca Egerton 1845; William Johnson 1846;
Benjamin 1848; Mary Ann 1850; Matilda 1853; John Wesley
1853; Elizabeth Victoria 1857; Samantha Lenora 1858 and
Albert Edward 1861.
In the 1790's there were not a lot of recorded Burley's
in Ireland. I think now that mine may have been from
Killesher. Looks like they did follow a naming pattern
and that too adds to my thoughts of a connection.
Please contact me off line to discuss this further.