What is the purpose of this unusual garment? As it does not keep the body warm or dry my only theory is that it is used to hold the fat in, can I be right?
Link to a picture of what kind of vest you mean?
Anyways, I imagine that people wear them for fashion reasons. i.e. there isn’t really a “reason” why they wear it. Why do people wear anything they don’t really need to?
I doubt Rab C. Nesbitt wore one for fashion reasons 
Here in the UK, they’re associated with old men. They’re the same shape as a normal vest, and worn under jumpers / shirts etc. They’re made from a material like this: ASOS | Online Shopping for the Latest Clothes & Fashion although that example is obviously purposefully “fashionable”.
My WAG is that the “holed” design allows for more air to be trapped between the skin and the next layer of garmet. Air is a good insulator, so a string vest keeps you warm without large amounts of material going into its making.
I don’t know - I think he looks very fetching
http://www.stuii.co.uk/images/sitesupport/rab-nesbitt.jpg
another reason to wear them is that it gives an illusion of being decent while staying very cool, e.g. for hot countries
Were they originally made at home? Seems to me someone with basic weaving/knotting/tatting skills could easily make one. Cheap AND useful, what more could you want?