1822/1826 Williams headstone says he was born in Edinburg. It also says he died at age 66 and three months in November 1892.
I wouldn't get too hung up on the ages - people frequently either didn't know their exact age, or chose to give it differently. William gives his age as 30 when he marries in 1858 - which would put his birth year at 1828 - but gives his age as 47 in the 1870 census, making his birth year around 1823...
I've been trying to track down William's siblings - so far, only have a semblance of luck with Catherine, who appears to marry a John Thompson in North Leith in 1841. Got quite excited at this point, wondering if this was the same family as Margaret Minto Thompson, but she's the youngest, born 1836 - so if John was her brother, he'd be unlikely to be getting married in 1841...
The census records for Edinburgh and Leith - and indeed for most of the Lothians - are a bit confusing around 1841 and 1851, as there were some district name changes - so I'm having trouble tracking down John Thompson and Catherine Hogg after they married. They do appear to have had a son, William, in 1843, who married Agnes Lawson in Auchterderran, Fife in 1865 - on the marriage cert, father John Thompson is deceased by this time - his occupation is down as gardener. One of the witnesses is a John Thompson - who could be a brother of William...
Not having much luck with the other Hogg siblings - thought I may have found Jean/Jane in Uphall, West Lothian in 1851, with father William and two seemingly illegitimate children

But I can't track that census entry down on FreeCen yet to see whether their transcription matches Ancestry's...
Onwards and upwards...
Ruth