The youngest Price child, Betsey is very spoiled by her mother and tends to run amuck in the household, not doing what she's told and stealing from Susan. She's a little kleptomaniac, or shop-lifter, in training. Actually, Betsey is in training to become a bit like another spoiled daughter as well: Maria Bertram. There are some definite similarities between the spoiled young Betsey and the type of indulgent treatment that Maria got from her Aunt Norris.
Betsey also connects Fanny to her lost past; Fanny explicitly compares Betsey to another little sister, Mary Price, who died after Fanny moved away. Symbolically, Betsey keeps stealing a knife (presumably something like a butter knife) that Mary left to Susan. Mary was Fanny's favorite sister, and in a way this battle for Mary's possession is a fight for the mantle of Fanny's favorite sister and for ownership of the fond memories of her past that Fanny tries to hang on to in an unpleasant present. Susan wins the knife finally and the spoiled Betsey is bought a new knife by Fanny.