After Jacob is given Isaac's blessing as leader, Esau is given the blessing that he shall "live by the sword". Some see this as another sign of Rome, famous for her unique sword made of steel - the gladius - that smashed its way to world hegemony and on the way massacred the descendants of Jacob/Israel.
Another explanation is that Esau is described by the Bible as ancestor of the Edomites, the Hebrews' neighbors (and on many occasions, enemies) to the south. King Herod, whom many Jews considered as a usurper and destroyed of the legitimate Hasmonean dynasty, was an Edomite (though converted to Judaism). And since Herod was a collaborator with the Roman rule, the ancestor of the Roman's collaborator becme became identified with the Romans themselves.
Later, when the Roman Empire turned Christian, Esau became perforce identified with Christianity and Christians. This was reinforced by the rise of Islam, whose followers outspokenly claimed Ismael as their ancestor. This created for Jews a neat symmetrical view of history, with each of the competing monotheistic religions identified with a brother of a Jewish Patriarch (Ismael, brother of Isaac, and Esau, brother of Jacob).
