Edom’s sin seems to be the harbouring of a perpetual and continual grudge against Israel. They bought Israelite slaves from the Philistines (Amos 1:6) and possibly sold them to Tyre (Amos 1:9). In all their actions they did not treat the people of Israel and Judah in a manner that recognized their historical ties to one another.
11 Thus says the LORD: “For three transgressions of Edom, and for four, I will not revoke the punishment, because he pursued his brother with the sword and cast off all pity, and his anger tore perpetually, and he kept his wrath forever.