Excellent question! In the fourth part of the novel, the tone finally turns to a more hopeful one. Laila discovers that Tariq is alive; she and Mariam escape Rasheed (though it is through violence), and Laila and Tariq not only begin to recognize a more optimistic future for themselves and their family, but they also hope that Afghanistan might once again demonstrate the civilized and cultured nature that it possessed during its Golden Age. Present tense for this portion of the novel illustrates the characters' ability to put the past behind them and live in the present.
In contrast, Hosseini's use of past tense for the earlier parts of the novel can be interpreted in several ways. First, Afghanistan under Taliban rule is a country chained to the oppressive ways of the past. After the Soviet withdrawal and the rise of the Taliban, the nation literally goes back in time, something that has not occurred often in global history. Women are treated as possessions. Their clothing changes from the modern westernized clothing of the 1970s to burqas, and technology that was once readily available in Afghanistan is banned or sold as contraband.
Similarly, Hosseini most likely writes most of the novel in past tense to demonstrate how one's past affects his or her future. In Mariam's case, her mother's past and her own past with her father dominates everything in her married life--from her lack of self-esteem to her relationship with Rasheed. Laila's happier past with a doting father allows her to maintain a more hopeful outlook on life. Even though she endures much at the hands of Rasheed, Laila is able to recall fond memories of her father and of Tariq which sustain her until the book's fourth section. The author's presentation of two very different backgrounds (or pasts) demonstrates that an individual's history influences his or her present and future. Hosseini doesn't use past tense to argue that a person's past controls his or her future--for Mariam is able to stand up for herself and prove her self-worth--but he certainly illustrates the significance of past influences.