However it might end, he was without any question their pleasantest acquaintance in Bath; she saw nobody equal to him; and it was a great indulgence now and then to talk to him about Lyme, which he seemed to have as lively a wish to see again, and to see more of, as herself. They went through the particulars of their first meeting a great many times. He gave her to understand that he had looked at her with some earnestness. She knew it well; and she remembered another person's look also. Ch.16

These are all signs of a deepening interest. But just when we think Mr. Elliot might come to replace the dashing Captain in Anne's heart, we get to this part...

The same image of Mr. Elliot speaking for himself brought Anne to composure again. The charm of Kellynch and of "Lady Elliot" all faded away. She never could accept him. And it was not only that her feelings were still adverse to any man save one; her judgment, on a serious consideration of the possibilities of such a case, was against Mr. Elliot.
Though they had now been acquainted a month, she could not be satisfied that she really knew his character. Ch. 17