I have tried the Ulster Historical Foundation ie
www.ancestryireland.co.uk/ sorry no 1851’s for birth
Birth Record Wightman John 1842 Co Down
Births Wightman John 1870 Antrim
Birth Record Wightman John 1872 Co Down
Birth Record Wightman John Mains 1882 Co Down
Births Wightman John Dunseith 1907
.
Or his father if names the same might have married in same year or before
Civil Marriages Wightman John 1850 Down
Civil Marriages Wightman John 1851 Down
Civil Marriages Wightman John 1851 Down
Marriage Record Wightman John 1851 Down
Marriage Record Wightman John 1851 Down
from
www.family search.com has no irish John Wightman births 1850-1852
I have tried some scottish websites to find your information.
on
www.caora.net if you do a surname search not a message search, there is a big list of Wightman clues.
which census did you find him under and is there not other info about him, ie location in Scotland married children etc.
are there other census that you haven’t checked?
So the best clues above is in the marriages I think, and that will be a fee lookup from UHF
Good Luck Jim