I believe it is their personalities -- Mr Knightley was a forthright man, while Mrs Weston was naturally gentle. A governess was expected to exercise some authrity over her pupils, but -- chap 1 -- "Even before Miss Taylor had ceased to hold the nominal office of governess, the mildness of her temper had hardly allowed her to impose any restraint". She had "fallen little short of a mother in affection", but as Emma grew older, "it was more the intimacy of sisters."

She was Emma's mother figure who was perhaps over-indulgent and later became more like a sister.