At a private party Prince Charles reportedly ended his speech saying: "My darling old Harry, I’m so happy for you."
Now why would a father call his son "old"?
It's not an unprecedented usage. When my late sister Jack left her husband for another woman, her husband, Gary, and she remained on very good terms. That lasted all her life. He was at her bedside when she died of breast cancer a few years ago. A truly lasting and affectionate friendship. Better than many marriages. She kept his surname too. And Gary would often refer to her as "old Jack", although they were about the same age.
So it is clearly an affectionate usage but is there more to it? I think there is and I am open to suggestions about it. I think it is respectful too. It shows a respect for the other person's competence and individuality.
The Cockney expression "old cock" might also have some of that meaning, I think. Amusing if a Royal Prince got the expression off Cockneys