That is a 'depends' answer.
The origins of who pays depends on the outlook. It breaks down thus:
Wife's Family pays: The father is paying an added thank you for the groom taking the bride out of the household so that food and living expenses are less, and to add to their beginning life so that the bride might have a home or better home.
Husband ('s Family) Pays: To prove that he can provide for the bride, and to give the bride something to fall back on should the marriage fail [also provides for her should the marriage fail since the thought is it would ruin her chances for marriage, having been rejected once already].
AND origin of country effects the answer .... want to be traditional? Pick one and enjoy :D
Dowry.
It has been an Asian tradition for the family of the bride to give the groom's family a dowry. A dowry serves as a gift for the groom and his family for marrying a girl. A dowry can be in kind or in monetary form.
In ancient Greece, a dowry was a payment or gift given by the bride's family to the groom as part of the marriage agreement. It served as a form of financial security for the bride and helped to establish the social status of both families involved. The dowry was often used to demonstrate the bride's family's wealth and to ensure the bride's well-being in her new household.
A dowry is given to a prospective groom from the bride's family. This may have been money, livestock or valuable goods.
A dowry system is something that is used often in India. This is where gifts are given to a bridegroom's family in exchange for the bride to be married to the man.
The practice of wrapping the feet of women was instituted during this era. Supposedly, the feet were to represent the Lilly flower and thus garnered a higher dowry when the women was given for marriage.
It is a widow (female).
In 1468 King Christian I of Norway gave the Orkney Islands as a security for his dowry of his daughter Margaret who was betrothed to James III. The dowry was never paid.
A dowry is either property or money given to the husband by the bride on their wedding. The practice is used as tradition in India but it was not allowed until after 1961. Some have questioned the ethical side of it, as sometimes women may have control of the money after the wedding.
girls required a good musical talent to secure a good marriage
A dower slave is a type of slave who is given as part of a bride's dowry to her husband upon marriage. The slave would be owned by the husband and could be used for labor or other purposes. This practice was common in certain societies in the past but is now considered unethical and illegal.
If the father of the bride give the groom a large sum of money; a place in the father's business or land it is called a 'dowry.'