Esau's descendants lived in Edom. Edom (whose land was located south and east of Judah, between the Dead Sea and the Red Sea) was not destroyed by the Babylonians as Judah was, because its inhabitants sided with the Babylonians in their eastern campaigns of conquest. After Judah fell to the Babylonians, Edom took vengeance on Judah as repayment for years of domination (Ezekiel 25:12–14).
Because of the hardships that Israel faced upon returning from exile, and because Israel saw that Edom fared better than they did, it seemed to the returned exiles that God’s special love for Israel had ceased, and that God loved the descendants of Esau more. God disproved this, however, by raising up nomadic tribes of Arabia, who dispossessed the Edomites. The fact that the Israelites had returned to their own land, while the Edomites had been dispossessed, was proof of God’s unfailing love for Israel.
3 but Esau I have hated. I have laid waste his hill country and left his heritage to jackals of the desert.”