...how badly did they think of the Byzantines?
Pretty badly,
the Byzantines felt that the Western Europeans were still Barbarians,
While the Knights of Western Europe felt that the Byzantines were stuck up, and very tricky.
Where the Knights of Western Europe fought with fewer tactics,
the Byzantines were always using tactics to win the day.
Because of this,
And the ill feeling that the Byzantines already had towards them,
the Western Europeans did not like them very much.