The veil originated with the Assyrians. It sort of publicly branded women (for men's convenience) into the off limits ones and the ones that were fair game for the dudes in a patriarchal, militaristic society.
So it absolutely has origins from middle east though not derived from a God or Goddess, then or otherwise. I know that is very surprising! Goddesses and Gods keep changing over time, anyway. Most people who live in the region now would probably be regarded as atheistic or heathens by their ancestors for adopting alternative parvenue deities/idols. People can try dress it up how they like (pun intended), but it would still be bunkum.
There were two young women in the big headscarves on a channel 4 report. One was talking about her scarf and it seemed it wasn't simply an item of dress because it is associated with your 'modesty'. I guess like a badge or something. You wear this badge, you are extra good. I suppose, the patriarchy says so! I found it interesting when one of them kept going on and on about modesty whilst absolutely caked in a thick layer of make-up. What she meant was I am special and modest and get a gold star for my big scarf and am judging everyone who doesn't adopt it as whores or sluts. Ironically, I have heard other judgemental people who might describe her as a tart for her inch thick make-up, despite wearing what she regarded as a sacred garment bestowing modesty by simply using it for a head covering.
She was basically implying women who don't wear a big scarf on their heads like her are sluts (by saying she was wearing it for modesty and it made her a special modest woman) and some others, not taught that her headscarf bestowed modesty properties, looking at her caked in make-up and regarding her as a tart. Each in their own way useful idiots. Women vying to confer whore, tarts or sluts on each other simply because of the use or absence of artificial artifices. Who does this serve?
I've never heard a man being called 'immodest' for his garments or make-up. However, the most outline of a lunchbox I have ever seen was a guy streaming with a crowd towards a mosque. He had a long shirt dress on and obviously no trousers underneath. A strong wind contoured the dress cloth against his regions. His 'privates' stood very proud from the plane of his body. He would have been much more 'modest' in jeans.
In short, the claim it originated from some sort of religious commandment and has associations with the wearer's 'modesty' is twaddle. It is a piece of cloth on a head. Same rules regarding wearing any piece of cloth should apply. Make-up is also just stuff on a face. Being tarted up, doesn't make you a tart.
Lots of women mid 20th century used to wear a headscarf to keep their perm in place. Christianity and other religions/cultures were poisoned from the same chalice seeping from the Assyrians regarding a covered head is a 'modest' woman. However, I do like a beanie!
Lazy rambling over.