I believe that in days gone by, in England, the Church did not hold weddings and they forbade you to hold a wedding on Church grounds. Some people who wanted to involve the church got married in the church's lych gate.

My guess is that as the power of the Catholic Church grew, they spotted that countries were forming alliances by marriage. Kings in one country would marry princesses from another to bind those countries together. The Church hierarchy would realise that if they controlled marriages then they could control the global alliances. Enter the Church's rules on who is allowed to be married to whom - and priests would need to get involved.