From what I understand in the early church, at least since the time that the catechumenate became a much longer process with baptisms being performed only once a year on Great Saturday, they were only performed during the Liturgy of Great Saturday (during the Liturgy itself mind you, not before the service. This is a lot easier if there are two priests). Marriages were also done during the Divine Liturgy and I actually have the Greek Divine Liturgy/marriage service saved somewhere and it is quite beautiful. The prayers are litanies and said at various points throughout the liturgy. For the entire duration of the service the groom and bride stand in front of the iconostasis, the groom in front of the icon of Christ and the bride in front of the icon of the Panagia, and instead of the common cup used during the separate marriage service they both receive Holy Communion.
You will notice that both the separate baptismal and marriage services begin with the priest exclaiming "Blessed is the Kingdom of the Father and of the Son and of the Holy Spirit..." as opposed to "Blessed is our God always now and forever....", which reflects the origins of these two services as taking place during the Liturgy.
I am not quite sure why these two services became separate from the Divine Liturgy or when exactly it occurred, but I know that it is very uncommon for a marriage to take place during the Liturgy these days. I remember asking a friend in Greece about how common it is there and he told me about one instance where it happened, and how the relatives of both the bride and groom were complaining about how long the service was (which is quite possibly the reason that the separations from Liturgy occurred in the first place).