In the marriage registration of 2 June 1905, George Watson states that his parents are John Watson and Sophia Watson, M.S. Anderson.
But as noted above, Sophia Anderson married John Cheyne on 6 Jun 1885, and on that document she is Sophia Anderson, Spinster. They and most of their children emigrated to Canada in 1912 (following son James who had migrated in 1904-5 according to Canadian censuses). So she was Sophia Anderson to 1885, then Sophia Cheyne.
It seems therefore that George Watson concealed (or didn't know) the fact that his mother and father were not married. Given that her name is given as Skene in his death registration, they may well have lost touch.
Interestingly Sophia's other illegitimate child Anne Melvin did exactly the same thing - claimed her parents were married but they never did.
I have all the certificates from Scotland's people, but of course cannot publish them here - crown copyright and all that.