What was the Byzantine reaction to the Papacy declaring Charlemagne as Emperor? Did the position of the Eastern Empire change throughout the latter period of its life?
Could you elaborate on what you mean by 'Did the position of the Eastern Empire change'? Are you referring to its position towards the Holy Roman Empire, or something else?
To answer your question, I found a similar thread on this subreddit from years ago that seems to answer satisfactorily https://www.reddit.com/r/AskHistorians/comments/1hj2v6/how_did_the_byzantines_view_the_holy_roman_empire/