Why the "wedded" in "wedded wife"?

As far as I can tell, it's one of two reasons:

• According to the The History of the English Language, "wedded" in vows originally meant something more along the lines of "pledged". However, in Old English, wed had that meaning in addition to the meaning related to marriage.

• Looking at Middle English (usually outside of vows), "wedded wife" (and also apparently bewedded wife) was used a lot more commonly than "wedded husband". Quotes such as Orm's "weddedd wĕre & weddedd wif" illustrate why this is. The word "wif[e]" here means "woman", contrasted with "were" which translates to "man" (see also the Ormulum's full modern translation). At this point in history, a "wif[e]" could be either a woman or a married woman so not all examples are clear cut on which meaning is the most correct. However, I can say that "wife" was still used to mean "woman" (MED lists examples as late as 1475) when the first vows with "wedded wife" and "wedded husband" were made (about 1400). "Wedded wife" therefore serves to disambiguate, and "wedded husband" is there to keep it symmetrical.

Here are some early examples of "wedded husband":

• "For [ne] wille ich þe loue, ne non oþer, Bote mi wedde houssebonde." (Dame Sirith, a1300)
• "Dowtyr…take me to þe as for þi weddyd husbond, as thy derworthy derlyng & as for thy swete sone." (The Book of Margery Kempe, Book 1, a1438)

Historically and etymologically, "wife" meant "woman" (and "husband" meant "householder"). The word was used for both "female spouse" and "adult female" up until at least Middle English (late 1400s), and the 1911 Century Dictionary still has this:

1. A woman: now only in rural or provincial use, especially in Scotland, and usually with an adjective, or in composition with a noun… as, old wives’ tales; a fishwife.

So it seems very plausible (though not certain) that "your [lawfully] wedded wife/husband" was included in marriage vows because, otherwise, it might have implied a relationship that wasn't binding or wasn't Church-approved—as "your woman/man" might in modern English.

It's worth noting that it's still somewhat redundant, given that the rest of the vow spells out the details of the commitment (and, in older forms, the Church's approval). So the authors of wedding vows weren't aiming to be concise and avoid repetition. On the contrary, they probably wanted to state things several times in several ways, to ensure everyone grasped the seriousness of the event!

First, it is important to state that The Common Law of England did not, and does not, recognise "common law" marriages.

The OED has another definition of Wife:

5. A woman who has a long-term sexual relationship with a man to whom she is not married; a mistress; a concubine.

1679 Domestick Intelligence 2 Dec. He hath lived with a wife or woman for some years, by whom he hath had two or three children.

Note the use of "a" wife" that indicates a random example of a cohabiting woman rather than any formal relationship with the man.

A cohabiting woman may be referred to as a "wife" but she is not a "wife" in the eyes of the law or the Church (The law and the Church were much the same thing.)

The OED continues:

In early use chiefly with reference to the concubines of priests. In early use, the marital status of these was still a matter of dispute;

As the clergy wrote the Book of Common Prayer, the Church wished to distinguish between (i) these "priest wives" and any similar women referred to as "wives" who had (arguably) not been through a recognised marriage ceremony and (ii) women who had been officially "wedded" to a man.

A "wedded" wife was thus a woman who had been through a recognised form of marriage (at the time there was only one form.)