Vesime is a comune in the Province of Asti in the Italian region Piedmont, located about 60 kilometres southeast of Turin and about 30 kilometr…Vesime is a comune in the Province of Asti in the Italian region Piedmont, located about 60 kilometres southeast of Turin and about 30 kilometres south of Asti. As of 31 December 2004, it had a population of 683 and an area of 13.5 square kilometres.