Upvote:3
Generally speaking, you could apply following rule of thumb- higher the position of women in society, higher the dowry. This is not universal, and there are exceptions, but it is mostly true. We will go by examples :
In Christian societies, especially as you mentioned in Roman Catholic Italy, marriage was monogamous and usually for life. Yes, there were extramarital affairs, but divorce was especially hard to get (remember Henry VIII and his breakup with Catholicism) .This means that essentially groom was stuck with his lovely wife to the rest of his or hers life. And, if he was from a wealthy family (nobility or rich merchants for example) his wife would have to be given proper rank, respect and most importantly expenses. Her children would be his successors, again with their own expenses. Financially speaking, woman would be a burden, especially in a rich family where she would not work as much as for example peasant's wife . Although even among poor peasants usability of women for hard field work was much lower then usability of men of her age (on average of course) . From the point of the bride's family, they would have less financial burden, and usually their daughter would not inherit any property if married (except dowry given at the wedding) . Furthermore, her offspring would inherit property of another family. All of this combined makes the case for the dowry to be payed by bride's family.
In polygamous societies, value and position of a woman is much lower. Not to paint with too broad of the brush, but for example in Islam woman is essentially slightly better then chattel. Man, especially rich, could have many wifes, use them for his sexual pleasure, is not under obligation to recognize their children as his heirs, and could legally divorce them. Exactly for this reason, dowry called mahr is actually payed by the groom, as some sort of security for the bride in case of divorce or groom's death. Essentially, in polygamous societies man would "pay to play" with certain woman, because his obligations toward her would be much diminished.