I maybe reading into NA more than the author intended but we are all aware how subtle are the depths of Miss Austen's works.
I personally think much of Rev Tilney's good-natured teasing and quizzing is his sizing up Catherine's suitability to be his wife.
There is no guile in Catherine and he finds her refreshingly candid, transparent, and unaffected. Yes, even her paranoia over the fate of Henry's Mother is all youthful innocence and ignorance.
I also think Henry considers Catherine a diamond in the rough, much like Emma. She has all of the innate qualities Henry already loves and she will only improve and thrive under his tutelage.
Growing up in a large happy family, her candor and unselfishness will make it easy for the parish to love her.