Genesis 16:2

it may be that I shall obtain children by her Heb. lit. be builded by her; the same expression occurs in Genesis 30:3; the idea is that of the building up of a house (cf. Ruth 4:11; Deuteronomy 25:9). The suggestion which Sarai here makes, may be illustrated from Genesis 30:3-4; Genesis 30:9. Childlessness was, and still is, in the East, a great reproach (cf. 1 Samuel 1:2-20). It was the custom also in Babylonia, as is shewn by the Code of Hammurabi, that "if a man's wife was childless, he was allowed to take a concubine and bring her into his house, but he was not to place her upon an equal footing with the wife. Or, the wife might give her husband a maidservant (amtu), and, if she brought up children, he was forbidden to take in addition a concubine" (S. A. Cook, The Laws of Moses and the Code of Hammurabi, p. iii).

by her By the adoption of Hagar's children as her own.