Albert Barnes Commentary Psalms 45:7

"Thou hast loved righteousness, and hated wickedness: Therefore God, thy God, hath anointed thee With the oil of gladness above thy fellows." — Psalms 45:7 (ASV)

Thou lovest righteousness ... - See this verse explained in the notes at Hebrews 1:9, where it is applied to the Messiah. The word "God" is rendered in the margin "O God"; O God, thy God, hath anointed thee, etc.

According to this construction, the thought would be carried on which is suggested in Psalm 45:6, of a direct address to the Messiah as God. This construction is not necessary, but it is the most obvious one.

The Messiah—the Lord Jesus—though he is described as God himself (John 1:1 and other passages), yet addresses God as “his” God, John 20:17. As Mediator, as appearing in human form, as commissioned to perform the work of redemption and to subdue the world to the divine authority, it was proper thus to address his Father as “his” God, and to acknowledge Him as the source of all authority and law.