I found this explanation from Ayatullah Mahdi Hadavi Tehrani useful:
"The reason that the inheritance of man is more is because the upkeep of women is upon the shoulders of men. In other words, aside from the fact that a man must look after himself, he is also responsible for the upkeep and expenses of his wife and children. From another point of view, it is the man who gives the dowry to the woman and she is the one who takes it from him.
In reality, it is possible to say that what the woman takes in the form of inheritance and dowry is tantamount to her savings, whereas the portion of the inheritance of the man is spent on the expenses of his daily life and that of his wife and children. Aside from this, certain other responsibilities have been placed on the shoulders of a man, which necessitate his spending money in order to carry them out.
For example a man must spend money in the way of war, or if one of his relatives accidentally kills someone or injures someone he must pay certain monies to the family of the victim, whereas a woman has no responsibility in this regard. So even though what is apparent is that the share of a man in inheritance is two times that of a woman, in all practicality his share in the sum total of personal wealth is far less than hers. While on the other hand, in exchange for the “excess” inheritance, man has heavier responsibilities to shoulder than a woman. So in brief it can be said that the inheritance of men and women being different is so as to implement a sort of balance between the rights and responsibilities of each group."