What are the benefits of Polygamy marriage over monogamy?

Plural marriage allows for a larger pool of income for families-- three incomes are better than two.
It also allows for a woman to strive for her career, even with a child. Usually the mother takes greater care for the child and will have less options and time for a career; if there are two or more women in the family, the child will still be properly cared for by family while the mother is working. (Like a built-in day care, except without putting the trust into strangers)

Women won't face as much sexual pressure- there is less of an reason for the man to pressure his wife into sex when he can ask a different wife.

Many people have extramarital affairs anyways during monogamous marriages. Having the option of polygamy will make it so the person's other partners will have legal rights to their partner.