Mother in Israel has been doing a great job translating an article about the latest chumrah, stringency--not always accepted by the mainstream (though sometimes they become popular and considered Law,) the obsessive-compulsive, much moreso than the Moslem women's body covering fringe-fad among some religious Jewish women.
In this Hebrew article from Maariv, Neshot Hare'alah (Women of the Veil), Sherry Makover-Balikov interviews Rabbanit Bruria Keren and some of her followers.Part I, Part II, Part III, Part IV, Part V, Part VII
To see all posts on the subject click on the label hyper-tzniut.
As far as I'm concerned, it's no more Jewish than the idea that men are supposed to be cloistered away in Batei Medrash learning Torah day and night, while their wives have to earn a living.
Considering how insecure many "new" chareidim are about how "perfectly" they're keeping the mitzvot, I presume that this will spread.
For a couple of months, I studied in the very beginnings of Neve Yerushalayim, January, 1971, until a student became ill with tzahevet, jaundice. I was then pregnant and quickly fled. I remember a student announcing that she was attempting to keep every chumrah she heard about, in order to be as religious as possible. Quickly, one of the teachers explained that according to halacha, Jewish Law, a single woman can/should not do it. A woman "inherits" customs, and chumrot are technically only customs, from their fathers or must adopt them from their husbands.
According to the article, it seems that most of the "veiled" women are either converts or newly religious.
*The article quotes one of the followers saying that just like tights on little girls, which it claims is a very new rule, is now required, the total body cover will become a normal accepted dress code. This isn't true at all. Chareidim demanded tights on little girls even in the summer over 30 years ago, when my daughters were in Gan Ruti, Bayit Vegan. Not that she threw them out for not complying. It was a private gan, and she needed every kid to make a living.