In A Thousand Splendid Suns by Khaled Hosseini, how do the relationships between the characters highlight the concerns of society?

While there are many relationships in the novel, perhaps Laila's relationships reflect society's concerns most directly. To begin, she has been raised by forward-thinking parents who taught her to value herself as an intelligent person, not merely as a potential wife.  Such a woman was certainly concerning for the powers-that-be in Afghanistan, since their system required the subjugation of woman. Such a society feels threatened by citizens who raise their children to oppose the status quo. The qualities that Laila gains--self-confidence, leadership, a sense of compassion and morality, and perseverance--all deeply affect the relationships she develops after the death of her parents. 
Indeed, Rasheed is startled to encounter a wife who will not bow to his dictatorship but rather opposes and outsmarts him, even turns his first wife against him. Try as he might (through tactics too horrible to consider), Rasheed cannot break Laila. However, through her unfailing perseverance and demand for human decency, Laila inspires Mariam's love and loyalty in a way that Rasheed's immoral fear tactics never could.  In fact, Laila inspires Mariam to evolve from a victim, so compliant to society that she would never consider trying to help herself, into a woman who opposes the system (Rasheed, in this case) in order to protect those she loves. Strong leaders inspire change, especially where it is desperately needed.
This is also true in any given society.  A government might rule for a time with fear tactics, but they will never inspire the affection and loyalty of their people.  The Taliban cruelly beat Laila for breaking the rules, but she simply determines to find a new path to the orphanage to see her daughter, Aziza. Oppressed citizens are often forced to break the "laws" in order to meet their needs and those of their loved ones. A society based on dysfunctional relationships between the government and its people will never be a truly healthy system and will eventually fail. 
http://uwf.edu/atcdev/afghanistan/society/Lesson3GenderRoles2Women.html