Hey there—I'm not qualified to speak as to the fashion trends that influence styles (beyond that there exist different types of veils that cover different amounts of the woman). However, I can talk a little about the history of veiling in the Middle East. I'd recommend that you look into the book Women and Gender in Islam by Leila Ahmed if you're interested in more about the subject.

Veiling was common practice in multiple pre-Islamic societies across the Middle East and practiced, at least to an extent, among certain tribes of Arabia itself. In Assyrian culture, wearing a veil separated 'respectable' women and those who were commoners of unclean. Upper class women, concubines accompanying those women, and former "sacred prostitutes" were all required to wear a veil. Conversely, "normal" prostitutes and slaves were forbidden from veiling themselves under threat punishment: either a flogging or having their ears cut off.

Ahmed then writes that this practice spread throughout the upper-class Mediterranean world—from the Levant through to Persia—and simultaneously crossed religious lines. For example, Ahmed gives the example of a 10th century Byzantine Christian patriarch who wrote that he only allowed his daughter to go out "veiled and suitable chaperoned". She notes the reasoning—separating the respectable from the rabble—largely remained constant throughout societies.

However, the presence of the veil in the greater Middle East and Levant is not to say that veiling was necessarily widespread in Arabia itself. Women of the Jahilyya pre-Islamic period did not normally don a veil, with limited exceptions among certain tribes and within urban environments. While still nowhere near as common as in neighboring Syria or Palestine, women in cities in Arabia were more likely to veil than those in the countryside.

While veiling is now extremely common among devout Muslim women, the practice did not gain traction within Muhammad's life. Indeed, during his lifetime, the only women who were regularly veiled or secluded were his wives. The veiling of Muhammad's wives was brought about through a succession of revelations that he received, but remained unique enough for the phrase "she took the veil" to become synonymous with "she became a wife of Muhammad".

Various impetuses pushed Muhammad towards these revelations. For example, Muhammad was allegedly annoyed with guests staying too long after dinner to speak with his wives. Sura 33 Verse 54 was then revealed, detailing that one should only speak to Muhammad's wives from behind a curtain. The word he uses for curtain is ḥijāb. Most westerners associate the word hijab with some sort of head-wrap of veil, but it also literally can mean 'veil' in the sense of a curtain.

There were other, more series reasons for the commandments to veil. Verse 59 gives the commandment to women to "bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused." This is allegedly in response to the "hypocrites", mere nominal converts to Islam, harassing Muslim women and protecting themselves by claiming to have thought they were slaves. The practice of veiling was meant to distinguish women as upright Muslims, not slaves.

So why did veiling spread beyond the wives of Muhammad? Ahmed notes that there was no one impetus that increased veiling after Muhammad's death. She posits instead that it was a combination of factors: increasing Islamic conquest of urban environments where veiling was common; the resulting increases in wealth and status of the Arabs (hearkening back to the "respectable versus rabble" distinction); and a trend towards viewing the actions of Muhammad, and his wives, as sources of imitation.

Despite all of this, it was still not something that was necessary for women to do. Throughout Islamic history, you will find stories of women who veiled and women who did not. To give but one example, Ahmed mentions a well-respected, female medieval Islamic teacher of the hadīth, Hajar, specifically to point out that she taught without wearing a veil. This was allegedly a practice "common among many old women" and did not prevent (most) students from seeking her out for her expertise.