The rise of the Amorite kingdoms in Mesopotamia brought about deep and lasting repercussions in its political, social and economic structure, especially in southern Mesopotamia.  The division into kingdoms replaced the Babylonian city-states in southern Mesopotamia. Men, land and cattle ceased to belong physically to the gods or to the temples and the king. The new Amorite monarchs gave or let out for an indefinite period numerous parcels of royal or sacerdotal land, freed the inhabitants of several cities from taxes and forced labour, which seems to have encouraged a new society to emerge: a society of big farmers, free citizens and enterprising merchants, which was to last throughout the ages. The priest assumed the service of the gods and cared for the welfare of his subjects, but the economic life of the country was no longer exclusively (or almost exclusively) in their hands.  In general terms, Mesopotamian civilization survived the arrival of Amorites, as the indigenous Babylonian civilisation had survived the short period of Gutian dynasty of Sumer's domination of the south during the restless period after the fall of the Akkadian Empire that had preceded the rise of the Third Dynasty of Ur (the "Neo-Sumerian Empire"). The religious, ethical, technological, scientific and artistic directions in which Mesopotamia had been developing since the 4th millennium BC were not greatly affected by the Amorites' hegemony. They continued to worship the Sumero-Akkadian gods, and the older Sumerian myths and epic tales were piously copied, translated, or adapted, generally with only minor alterations. As for the scarce artistic production of the period, there is little to distinguish it from the preceding Ur III era.  The era of the Amorite kingdoms, c. 2000 - 1595 BC, is sometimes known as the "Amorite period" in Mesopotamian history. The principal Amorite dynasties arose in Mari, Yamhad, Qatna, fairly briefly in Assyria (under Shamshi-Adad I), Isin, Larsa and Babylon.  Babylon, originally a minor state at its founding in 1894 BC, became briefly the major power in the ancient world during the reign of Hammurabi in the first part of the 18th century BC, and it was from then that southern Mesopotamia came to be known as Babylonia, the north long before it evolved into Assyria.

Answer this question "Why did Amorites hegemony did not have effects ?" by extracting the answer from the text above.
They continued to worship the Sumero-Akkadian gods, and the older Sumerian myths and epic tales were piously copied, translated, or adapted, generally with only minor alterations.