Why did Byzantine Emperors usually not marry into European aristocracy? Especially with the increase in Ottoman aggression one would think they would seek more alliances with the west. I know that there were occasional marriages of Byzantine princesses to nobles in Western Europe - mostly to Hungary and Bulgaria. But I can not think of any "great" empress that came from a noble house from e.g. France or the Holy Roman Empire.
Ultimately the Byzantine Empire was less concerned with the West in general, they saw Constantinople (Istanbul) as the centre of their territory. They fought more wars with the Persian Sassanian Empire, continuously gaining and losing the same area of land above the Arabian peninsula. This shows that they were looking less toward the West. Equally, their Empire was vast and involved a lot of splintering due to slightly differing interpretations of Christianity so cementing internal relations rose in importance.