Thank you Kathleen. (:D) I think Mr. Knightley lives up to his name. He is attentive to the Bates and Miss Fairfax by calling, sending his carriage for them and contributing what he “ought to the stock of their scanty comforts” (19) and also trying to get Emma to do the same—IMO not only for their sake but Emma’s as well. Mr. Knightley will even oblige Mrs. Elton:

"You had better explore to Donwell," replied Mr. Knightley. "That may be done without horses. Come, and eat my strawberries. They are ripening fast."

If Mr. Knightley did not begin seriously, he was obliged to proceed so, for his proposal was caught at with delight; and the "Oh! I should like it of all things," was not plainer in words than manner. Donwell was famous for its strawberry-beds, which seemed a plea for the invitation: but no plea was necessary; cabbage-beds would have been enough to tempt the lady, who only wanted to be going somewhere. She promised him again and again to come -- much oftener than he doubted -- and was extremely gratified by such a proof of intimacy, such a distinguishing compliment as she chose to consider it. (42)

Mr. Knightley’s dancing with Harriet was the right thing to do but also has an aura of chivalry—he termed Mr. Elton’s behavior “unpardonable rudeness” (38) and he immediately steps up to counter it. I think it is possible he felt his previous opinion of Harriet re Mr. Martin was unjust because he did not know her well enough to understand her merits. He had said she is “pretty, and she is good tempered, and that is all” (8) and that the advantage of the match was all on her side:

My only scruple in advising the match was on his account, as being beneath his deserts, and a bad connexion for him. I felt, that as to fortune, in all probability he might do much better; and that as to a rational companion or useful helpmate, he could not do worse. But I could not reason so to a man in love, and was willing to trust to there being no harm in her, to her having that sort of disposition, which, in good hands, like his, might be easily led aright and turn out very well. (8)

I feel that after Harriet and Mr. Knightley’s dances their acquaintance is on a bit more “familiar” level and that alone would prompt him to talk to her more than he had done previously but I think what Harriet finds particular in his behavior does stem from an investigation into her feelings for Mr. Martin. There could be several reasons for this endeavor because I don’t picture Mr. Knightley as a matchmaker for the sake of making matches.

Perhaps when he found Harriet to be a better young woman than expected he might have also realized just how easily led she is—how easily led she was by Emma and felt more for Mr. Martin’s loss and perhaps Harriet’s as well. He knows that Mr. Martin was “very, very bitterly disappointed” (12) in being rejected and I can’t imagine he thinks Harriet will ever get a better offer so he may believe in trying to resurrect the attachment that he is not only doing them a good turn but correcting Emma’s error.