I did a little research on this. In pre-Christian Roman culture, a couple would be married by saying certain words in front of a pagan priest. Bridal consent was necessary, which she gave by saying "Where you are Gaius, I am Gaia". (I do not know if they changed the names depending on the grooms name. Roman women were not given real names at birth, as I understand it. They were given a feminine form of their fathers name, and distinguished by 'major' if older' and 'minor' if younger, or numbered if there were more than two.)
I have also read that the custom of women wearing a ring on the wedding ring finger was also a Roman custom.
My theory is that the Romans Christianized the wedding ceremony, replacing the pagan priest with a Christian one, but keeping the general format of saying words in front of a religious leader as a wedding ceremony. I guess the groom carrying the bride away, pretending to steal her as legend said the early Romans did, did not catch on as a part of the ceremony.
In OT weddings, there is no priest figure binding people together. The idea that a priestly figure makes two people one flesh by declaring it is not a Biblical concept. The wedding ceremony of the west is a cultural practice, not a Biblical one. That is not to say that it is bad. As far as I know all cultures have wedding rituals. In this ritual, there is a lot of scripture reading, references to God, imo a good thing. But it is wrong, imo, for people to say that if you have not said your vows before a preacher, pastor, etc. that you are not really married.
In the OT, the groom, or his father, would go to the potential bride's father or guardian, and negotiate a deal for her that included a bride price. Some time later they would be joined. It was the custom, at least by Samson's time, to throw a feast. if a man took a woman as wife, he slept with her. According to Paul, two being one flesh as to do with sex, and not with a preacher declaring it so.
The only wedding ceremony that I know of in scripture that gives any details is that of Boaz and Ruth. Boaz met with a relative in front of the elders of the city to redeam another dead relatives estate. He said with the elders witnessing that, as a part of the deal, the widow Ruth became his wife.
I suspect elders did not play a specific role in OT weddings, except to sit in seats of honor at the feast. In a Lavrite wedding to ones deceased relative's wife, if someone passed up on the opportunity to raise up seed, the woman was to bring him before the elders, remove his sandal, and spit in his face. Maybe that is why the elders were called in in Boaz's case, or because it was a legal trasaction.