The tradition of the bride's family paying for a wedding evolved from the system of dowries. Dowries were a price the bride's family paid to her future husband for her support and as a measure of good faith between the two families.
For much of history, women could not inherit or own property. It was necessary for fathers to marry off their daughters in order to protect wealth, property and land. When the a suitable husband was found, a price was negotiated in exchange for a daughter's hand in marriage. This allowed families to form alliances and prevent their wealth and assets from being lost. Since a female's family was responsible for securing her a husband, the wedding expenses were also paid by her father. Although they have all but disappeared in Western culture, dowries are still common in several Asian countries, most notably in India.