As a nation state, Italy has emerged only in 1871. Until then the country was politically divided into a large number of independant cities, provinces and islands. The currently available evidences point out to a dominant Etruscan, Greek and Roman cultural influence on today's Italians.
Your question involves statistics but what you want to know can best be described as "hearsay" There is a website that has more exact data on the subject. In answer to your question First cousin marriages in Italy in the late 1800's were few and far between and represented less than 1% of Marriages in a synopsis of the website www.gutenberg.org/files/29955-h/29955-h.htm
The Italian parish records usually say that special permission was obtained. Often because the bride was pregnant. I researched a case where an uncle married his niece and special permission was requested from the Vatican.
Remember that during the 1800's in Italy, the marriage was arranged by the parents, so boys and girls had not the chance to chose someone to marry, like nowadays.
At that time, parents arranged the marriage, and before the marriage the couple used to go to notary to write down a record stating what is brought in this new born family (properties, lands, houses, furniture, pots, dishes, beds, pillows, chairs, sheets and so forth)
So it was arranged by the parents, so the parents knew that the couple somehow had a solid future.
I hope it helps