As far as I can tell, she stops taking chems/disapproves of using them, that's the only noticable change.
Since I not going to recruit her yet, I don't have any personal experience of how her outlook changes.
I'm not a chem user, so I'm going to have to use other methods to win her approval.
There are a number of locks I've been unable to pick (lockpicking perk is low level), so I think at some point, I need to revisit everywhere I've been with Cait and pick the locks I couldn't open.
I'm not in the habit of taking money to help people out.
Also, there is the added complication that I'll have done every mission I can with Codsworth and Curie to earn their favor, which won't leave much for Cait to help with.
The only way I know of to check affection is to initiate conversation and ask their opinion of your relationship with them.
I don't think there is a visual indication anywhere.
There might be a console command to display it, but I don't know if there is one or what it is.