At the beginning of the story, we learn that Eva is Hannah's favorite aunt. In fact, there's a strong affection and bond between Hannah and her aunt.
As the story progresses, we learn that Aunt Eva never married. Instead, she lives with her brother (Hannah's Grandpa Will) and his wife (Hannah's Grandma Belle). Aunt Eva helped raise Hannah's father. When Grandma Belle was at work, Aunt Eva took care of the home and childrearing duties.
Because of Aunt Eva's selflessness and years of devotion, Grandma Belle willingly allows Aunt Eva to light the candles every Passover. Put another way, Aunt Eva is given the honor of lighting the candles to make up for the fact that she never married and thus, never had a household of her own. Throughout her married life, Aunt Eva devoted herself to her brother's household.
In addition, we get the sense that Aunt Eva appreciates the privilege of lighting the candles at every Passover Seder. As the story progresses, we learn that Aunt Gitl's niece Chaya sacrificed herself for Aunt Eva (whose real name is Rivka) at the concentration camps during the Holocaust. It was Chaya who took Rivka's place in the gas chambers.
Hannah is named after Chaya—this may be why Aunt Eva shares a strong bond with Hannah. When Aunt Eva lights the candles every Passover Seder, she remembers both the Jewish emancipation from Egypt and Chaya's sacrifice on her behalf.