I don't know if you are aware that there are various anomalies with Scottish research. For instance, an illegitimate child can have her fathers surname even if her parents never married. I think this is the situation here.
First, I think the Margaret Burk bc.1825 Glasgow - unmarried - shown as a lodger with Jessie and her husband in 1871 is in fact Jessie's mother thus confirming that Margaret Burk was never married to Jessie's father Robert Scott. Indeed, I think that Jessie was probably Margaret's only child.
We 'know' that Margaret Burk/e was Jessie's mother, that Peter Burk bc.1817 was her uncle, and that when Jessie married the 2 witnesses were a William Burk and Ellen Burk (I believe these were an uncle/aunt).
1841 Census - Barony, Glasgow
William Burk 50 Cotton Spinner b. Ireland
Margaret Burk 40 b. Lanarkshire
Peter Burk 24 Cotton Spinner ditto
Sarah Burk 20 Cotton Piecer ditto
Margaret Burk 24 ditto ditto
Ellin Burk 8 ditto
William Burk 4 ditto
1851 - 200 Main Street, Glasgow
Margaret Burk 50 widow born Glasgow
Peter Burk 33 Cotton Spinners Piecer ditto
Margaret Burk 28 (?) ditto ditto
Ellen Burk 17 ditto ditto
William Burk 15 Carter ditto
1861 cannot find any of the family anywhere.
1871:
Peter and his mother Margaret together at 181 Main Street, dau. Margaret with now married daughter Jessie - cannot find Ellen and William.
So, if Peter Burk is Jessie's uncle, his sister Margaret is Jessie's mother and, from census shown above, she was still unmarried in 1871(last sighting with Jessie).
Annette