Only-Begotten

From Anstey’s Doctrinal Definitions:

This is a term of endearment that an only child has in the affections of his father (Luke 8:4242For he had one only daughter, about twelve years of age, and she lay a dying. But as he went the people thronged him. (Luke 8:42); John 1:14; 3:16, 1814And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth. (John 1:14)
16For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. (John 3:16)
18He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God. (John 3:18); 1 John 4:99In this was manifested the love of God toward us, because that God sent his only begotten Son into the world, that we might live through him. (1 John 4:9)) or mother (Luke 7:1212Now when he came nigh to the gate of the city, behold, there was a dead man carried out, the only son of his mother, and she was a widow: and much people of the city was with her. (Luke 7:12)). Begetting, in the sense in which the word is used in this term, does not refer to a person's congenial beginning—his birth. A clear proof of this is that the Lord was “the only-begotten Son” before He was born into this world (John 3:1616For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. (John 3:16)). The emphasis in the term is on "only," rather than on “begotten.” Christ is the Father's one and only-begotten Son. Loosely translated, it could read: "dearly beloved One."
Hence, when the term “Only-begotten” is applied to the Lord Jesus, it is referring to His uncreated relationship with God the Father as His dearly beloved Son. It denotes the Father’s delight in Him. John 1:1414And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth. (John 1:14) speaks of the glory that men beheld in the Lord when they saw Him living in the enjoyment of His Father’s love. John said, in a parenthesis, that it is similar to that which an only-begotten child has with his father, having his father’s full and undivided attention and affection. (This is why "only-begotten with a father" is not capitalized in the text; it is referring to the human relationship of a father with his son, and the Spirit of God is using it to illustrate the affection the Father has for the Son.) Thus, the Lord was the Object of His Father’s undivided attention and delight (Matt. 3:1717And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased. (Matthew 3:17)), for He always dwelt “in the bosom of the Father” as “the only begotten Son” (John 1:1818No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him. (John 1:18); Prov. 8:3030Then I was by him, as one brought up with him: and I was daily his delight, rejoicing always before him; (Proverbs 8:30)) and “the Son of His love” (Col. 1:1313Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son: (Colossians 1:13)).