... the Bingley sisters like Jane as much as they like anybody - as far as that goes (not very far, I know!), they are sincere. As others have said, they need some companionship out in the wilderness, and Jane is the likeliest candidate. Also, as far as Caroline Bingley is concerned, I think it would be considered inappropriate for her to have only male companions once the Hursts have left, even if one of them is her brother, so she actually needs some female friends.