I always assumed (because ballads were often cleaned up) that he thought she had given him the pox (STD), and then she had to laugh because there was nothing else to do. ('put a brave face on it') Then of course she died of it as well, later, full of regrets. I am not putting this forward as a new explanation, but I would like it to be eliminated. It was also a common belief that a virgin could cure STD.

These Willie/William and Graham/Graeme names are common in southern Scotland, see Frazer's book 'The Steel Bonnets'. This book is concerned with the history of the same period.

Some versions that I have seen refer to him travelling to study. A southern Scots young gentleman could have gone/been sent to Reading to study, and there done what students commonly do (go a bit wild).