How did the holy roman empire impact the byzantine empire?

The Holy Roman Empire had a complex relationship with the Byzantine Empire, often marked by rivalry and competition for authority in Christendom. Following the Great Schism of 1054, the two empires drifted further apart, with the Holy Roman Empire asserting itself as a successor to the Roman legacy in the West, while the Byzantine Empire maintained its claim in the East. Additionally, the Crusades, which were often supported by the Holy Roman Empire, led to military confrontations and the weakening of Byzantine power, particularly with the Fourth Crusade's sack of Constantinople in 1204. Overall, the interactions between the two empires influenced political dynamics, religious disputes, and cultural exchanges in medieval Europe.