Even if we didn't know from Louisa May Alcott's biography and journals that Little Women is loosely based on her own family life, we'd probably know it from the affectionate tone that she uses to describe her characters. Each sister's personal struggles are described with loving detail, as though the narrator sympathizes with everything they're going through. Sometimes the narrator even goes to great lengths to explain where the characters are coming from and why they react to things the way that they do. For example, when Amy is struck by her teacher, Mr. Davis, as punishment for bringing pickled limes to school, she pretty much freaks out, and so do all her sisters. Her mom even pulls her out of the school. To us, that seems pretty extreme, and to nineteenth-century readers, who were used to corporal punishment in the schoolroom, it probably seemed laughable. But the narrator really wants us to understand why they react so strongly:
"To others it might seem a ludicrous or trivial affair, but to her it was a hard experience, for during the twelve years of her life she had been governed by love alone, and a blow of that sort had never touched her before." (7.40)
The narrator's affection for Amy and sympathy for her situation is strongly communicated to us in this example, as it is throughout the novel for each of the sisters.