"When the engagement of Frank Churchill and Jane Fairfax takes the Westons by surprise, Mr. Churchill readily admits he hoped for better for his son. Only when he is reminded of the character of Jane Fairfax does he reconcile that she is an eligible match for his son."

Do you possibly mean Mr Weston rather than Mr Churchill? All that we know about Mr Churchill's reaction is that he gave his consent with very little persuasion. If you do mean Mr Weston, he doesn't readily admit anything of the kind. Mrs Weston says it was their darling wish that Frank and Emma might become attached, but makes no comparison betweeen Emma and Jane. And I don't think that that wish had anything to do with class or money - just the hope that his son and her almost daughter might get together. IMO the Westons' main concern about the engagement is that Frank has broken Emma's heart. Once he is reassured on that point, Mr Weston also needs very little persuasion to approve the match and by Chapter 48 is "extremely anxious to shew his approbation to Miss Fairfax and her family".