Using Mr. Collins to illustrate how Elizabeth reflects the relationship between woman's identity and society is a little difficult because--essentially--Collins doesn't know what he is talking about! He therefore cannot be trusted at all on any point, including how society views and defines woman's identity. As Elizabeth says to Mr. Bennet:
He must be an oddity, I think, ... I cannot make him out. There is something very pompous in his stile. And what can he mean by apologizing for being next in the entail? We cannot suppose he would help it, if he could. Can he be a sensible man, sir?
Collins’ function is to make everything that comes out of his mouth seem ridiculous, and Austen succeeds admirably in doing just that. Yet let's suppose for a moment that Collins represents a sector of society that is as ignorant as Collins and that has the same ridiculous ideas as Collins has, which is right to do because Austen chose real types for her characters and drew them authentically without Dickensian caricature.
Collins represents a sector of society that views women as empty-headed beautiful angels who are not only irrational but also like to aimlessly toy with men's affections (perhaps like Dora in Dickens David Copperfield). This idea agreed with a broader sector of society that perceived women's identity as being bound up in the moral and physical management of the home and household. Charlotte provides a good representation of this identity, which is reinforced by Lady De Bourgh's continual instructions on how to do what when and how much to buy where.
Collins is the counterpoint to Mr. Bennet, who--despite his misguided ways and serious faults--who represents another small sector of society that allows a woman, as he allows his daughters, the personal freedom and psychological independence to embrace their autonomy and develop their humanity and dignity (of course Mr. Bennet's approach to this high and admirable though limited social trait worked out better for some daughters than others as guidance is always needed for any child of either sex).