Darcy
developed a good impression of her lively and cute manners, and
invited her to dance with him at another ball. Elizabeth agreed to
dance with him, and Darcy gradually changed his view of Elizabeth.
I persume that Elizabeth's inner beauty takes the fancy of Darcy, such
as her unique thoughts and kindness. She might be a woman that Darcy had
never seen before.
Maybe from your perspective, Elizabeth is impolite. However, Elizabeth treats everyone equally, and sometimes it appears to be impolite. I think her dignity won Darcy's heart.
What attracted Darcy first, I think, was Elizabeth's appearance,
grace and good manners. Maybe these attractive characters overwhelmed
the impoliteness Elizabeth showed later. Above al, it's hard to
explain accurately why someone loves another, isn't it?