Is there any? I know some companions dislike it, so I started travelling with Cait who doesn't nag me when I steal. But since there is no more karma, will there be any repercussions whatsoever for my stealing as long as I'm not detected?

Also, does Codsworth ever stop following you for doing things he doesn't agree on?

Since the karma has been removed I think the only thing it does is damages the "relationship" with companions, so if you travel with someone you keep upsetting you cant gain the maximum status if you keep doing stuff they dislike.

also, codsworth DOES leave your service if you keep doing stuff he dislikes.

Does he?

Every companion can leave if you piss them off enough. They won't attack you though.

I was fooling around before I turned of last night and Cosworth attacked me... I put him down three times and just kept coming...

Then it is a bug but yes they will. I have heard of Codsworth turning kill on sight while being stationed in Sanctuary which made camp building rather problematic. This was due to stealing in its presence.

Does anyone know if a companion's relationship with you will go down if you do something they dislike even if they're not with you? I asked Codsworth to follow me and it immediately said "Codsworth tolerates you."

Yeah some companions hate it.

If they are still in sight of you then yes it will affect the way they feel about you but the only time I have seen this has been in a camp where I keep all my companions that are not following at the time and me working at the workbenches. Preston likes it when you mod regular weapons and Cods likes energy stuff. Probably more but I have yet to get anything negative at a camp.