This is not an entry in a parish register recording a marriage. It is an entry from the roll of burgesses. Being made a burgess gave you special rights in a burgh and there were controls on who could become one. You could be made a burgess because your father was/had been one, because you had been apprenticed to a burgess and served your time, you might be made one as an honour or mark of respect (local landowners, visiting dignitaries etc.), or, as here, in right of your wife, she being the daughter of a burgess.
These rolls can be very informative. The Edinburgh ones go back to the late 15th century. The book is available on-line to read. The entry here gives the name of the man's wife and details of her father and grandfather. If I were you, I would look up the father and grandfather in the roll and that might give you names of wives or take you back to earlier generations.
