I think a proposal of marriage is pretty good proof of commitment, myself. I certainly understand those who think she was too quick to welcome him back, but ultimately, that is what served the plot. Since the story is not really about Bingley and Jane, once their estrangement is no longer necessary, Austen reunites them so as to tie up her neat happy ending. Elizabeth could not be really happy until her beloved sister is happy too, and therefore Jane must be happy.
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