What have been the major changes from the thirteenth century to the present with respect to marriage and society?

Obviously, the answer would vary depending on the particular society in which you are interested. Since no region is specified, this answer will address western Europe.

In the past 700 or so years, western Europe has evolved from a feudal society run by nobles to a groups of monarchies gradually evolving into nation states that have espoused liberal democracy. It has grown from an impoverished and war torn region to a harmonious one, with some degree of economic integration in the form of the European Union.

In the thirteenth century, the Roman Catholic Church dominated the religious landscape, with only a very small minority belonging to other religions. The religious landscape of Europe is very different now. Although Christians still form the majority among those who are religious, religious diversity is increasing and church attendance declining. Many different Christian denominations now exist. Religious institutions no longer dominate European thought or society. 

While gender inequality was common in the middle ages and it was considered extremely immoral to have a child outside of wedlock, such attitudes have become increasingly rare in Europe, where marriage rates have been declining, family size shrinking, and alternative living arrangements becoming more common. Gay marriage is legal in many countries and civil partnerships serve as an alternative to marriage.