William Beech comes from a troubled home environment, where he is physically and verbally abused by his mother on a shockingly regular basis. Without wishing in any way to absolve Mrs. Beech of any responsibility for her actions, it would seem that she has some kind of mental illness, a religious mania perhaps. She certainly sees William as full of sin, which she fervently believes needs to be beaten out of him at regular intervals.
It's telling that when Mrs. Beech dumps William on Tom's doorstep, she leaves him with nothing but a bag containing an old Bible and a leather belt intended for the boy's punishment. Clearly William's mother doesn't see anything unusual in her treatment of her son, and she expects Tom to carry on where she left off, savagely beating the young boy whenever he gets out of line. Further evidence of what appears to be mental illness on Mrs. Beech's part comes near the end of the story when William learns that his mother has committed suicide.