I always thought it was her betrayal of him that made him respect her.
Initially he was quite charming when trying to manipulate her but later he seemed to lose patience with her submissivness. He still used it it his advantage but it came across to me as though he viewed her with disdain because of her willingness to just blindly go along with what ever he wanted even if it meant betraying her crew which kinda makes sense given how Khan seems to take pride in how loyal his own people are to him.
By betraying him at a point when he was in control of the Enterprise she showed that she could be assertive and displayed a loyalty toward her crew that i think impressed him. At the end he seemed quite pleased by her betrayal so i think her actions made him open to viewing her as a potential equal rather than just a inferior being to be manipulated and used. Obviously in the years spent together on Ceti Alpha she was able to impress him further.
^ I like that line of thinking, Merlanthe.

