Elkanah went to Ramah to his house. The child did minister to Yahweh before Eli the priest.
The children of Israel in the passages just cited were forbidden, absolutely, to eat the fat of animals.  Furthermore, the priests were restricted to the breast and the thigh of animals sacrificed, and the sons of Eli brazenly disobeyed all these prohibitions.  They did not heed the admonition that violators would be "cut off" from among God's people.