I think that Anne's acceptance of CW and friendship with Charles Musgrove probably added to Elizabeth's disdain--not because Elizabeth was jealous that Anne was sought out, but because Elizabeth would have been revolted that Anne had such low tastes not befitting an Elliot. Elizabeth is all about consequence and appearance; Anne is all about genuineness, warmth of heart, appreciation of character--they are polar opposites in their motivations, and it stands to reason they would not be close. It would seem very inconsistent to me if the sisters were to be close, although I do think Anne wants to love her sister.