Dickens accomplishes his goal of eliciting sympathy from his readers for Magwitch in several ways.
First, when young Pip meets Magwitch, the escaped convict is pitiful. He is hungry, exhausted, shackled, and cold. While Pip is afraid of Magwitch, something about him still inspires a normally timid boy to help him. When Pip does help Magwitch, obviously, Magwitch does not forget it, and it is difficult as a reader not to be compassionate toward someone who offers undying gratitude.
Secondly, when Pip and Magwitch meet again after so many years, Pip's snobbishness toward the ex-convict cause the reader to side with Magwitch much as they do when Pip treats Joe poorly. Readers tend to cheer for the underdog, and Magwitch is definitely one.
As Pip begins to reach his full maturation, his attitude toward Magwitch changes, and he recognizes how much he is indebted to the older man. The reader wants Magwitch to feel that his money was was invested in Pip and that somehow his daughter Estella will love her long-lost father.