My experience recently:

I had a large checked bag - and was travelling First Class on Singapore. Checking in at Sydney - even though my luggage limit was 40kg, the Qantas (Handling Agent) rep would not allow a 31kg bag as they cannot accept bags over 30kg.

This is not on my ticket, nor in the SQ timetable but - again - Qantas is making up the rules for itself - and other airlines it appears.

I removed a book and then she accepted it.

Of course, when checking in at SIN for the way home, the book was back in bag and there was no problem! It even came off the belt at LHR about second!