Here in the Borders the capital is often pronounced "Edinburry" but again apart from Edinburghers (which I have heard) I can't really think of any other nickname for the folk. Aside from the obvious "Auld Reekie" I can't think of Edinburgh friends living hereabouts calling the city anything else. Never heard it being called "the Burgh" and to tell you the truth what I have heard most often is just people saying "we're going into town" which kind of confuses us Borderers as when we say that we mean the town nearest to where we live rather than a city 40 or 50 miles away. The memory plays tricks with you but 'weegie' is a pretty common usage. I take it Welch's use of it simply brought it to wider use outside of eastern Scottish working class vernacular rather than he invented it as such??