Understanding that the Roman Empire was very multi-ethnic by the time that the East/West schism happened, how "Roman" was Justinian or Constantine? Were they habitually marrying Roman citizens to keep as Roman as possible, or were they more often marrying local aristocracy to build local political power?
And what heritage would we consider those aristocrats? We're they more Greek, Anatolian Greek (i.e. Helleno-Turkish mix), or Turkish?
From a genetic point of view, they weren't romans. Justin ( the uncle of Justinian ) and Justinian himself were peasants from Bederiana, Macedonia. The origins of an emperor weren't that important, an exception could be Anastasius. When he was crowned the crowd chanted that they want a roman emperor. ( Probably because of the ex emperor was an isaurian and not so great. ) But even Anastasius was an albanian. As for marrying, some marry aristocracy. Anastasius married Ariadne to gain legitimacy as she was the wife of the ex emperor Zenon. As for Justinian, he married Theodora, who was a circus actrees and is described by Procopius as a prostitute. The difference is that Justinian was already co-emperor when his uncle, later adoptive father, Justin, was alive. So it was known who the the next emperor is going to be. Anastasius on the other hand was chosen by Ariadne and the senate and didn't had the same legitimacy as Justinian, so he married Ariadne for some extra.
The idea of a perceived cultural difference between Constantinopolitans and the provincial populations is an ongoing area of Byzantine political theory and one which is still very active now. So it is difficult to sum this up in a short answer.
Constantinople and it's cultural context allowed and actively encouraged intellectualism and the refinement of language to a state almost incomprehensible to those in the provinces. Constantinopolitans would have sayings like 'as difficult as teaching a Capadoccian to read' or declaring the Greek Christian people of Paphlagonia as barbarians in 1185. (Eustathios Archbishop of Thessaloniki). They saw a marked difference in ideas of education and standards of living.
Undeniably then this ostracised the people of the capital from their subjects and the events from 1180 to 1204 are a series of local rebellions of populations who can better organise their own defence than a self-interested and internally warring capital. Rhodes, Trebizond, Paphlagonia, Philadlephia, Bulgaria, Athens, Cyprus (some other differences in the last three) all renounced CP in favour of local government. In the aftermath of 1204 this allows for independent states and, speaking as a Byzantinist, very exciting work. The provincial strike back and declare Constantinople residents 'mules' on account of their dirty un-Greek/Orthodox bloodlines from Western marriages. They call back to ancient Greek examples and declare Anatolia their motherland. This is all the work of Dimiter Angelov and truly very interesting stuff. It was the work of John Vatatzes, Emperor of Nicaea to reforge bonds of loyalty with the people and create a new sense of representation for first Anatolia and then the Balkans. Sadly, when the Laskarid dynasty were deposed by the Palaiologoi and the little son of Theodore II blinded many of them again renounced the reconqueror of Constantinople Michael VIII as betraying the new Byzantine idea.
This is as much as I can write while waiting for a plane and it's my own specialism. However if you want earlier ideas of citizenship I recommend the Kadellis book Hellenism in Byzantium.