What is the italicization in the King James Bible supposed to do?
It makes no sense as stress, it seems to be random.
Italicisation in King James Versions and derivative versions are there to mark words 'added' to make proper English sentences, but are not individual words in the Greek or Hebrew base text.
It's not stress at all.
Originally, when the Bibles were printed in Black Lettering, these words were marked in Roman type. With the shift later on to set books in Roman type, then the words were put into italics. This remains common practice until the present.