Jamieson, Fausset and Brown on Hebrews 7:6

6. he whose descent is not counted from them--not from "the sons of Levi," as those "who receive the priesthood." This verse explains "without descent" (Greek, "genealogy" in both verses, He 7:3). He who needs not, as the Levitical priests, to be able to trace his genealogy back to Levi.

received--Greek, "hath received tithes."

blessed--Greek, "hath blessed." The perfect tense implies that the significance of the fact endures to the present time.

him that had--"the possessor of the promises," Abraham's peculiar distinction and designation. Paul exalts Abraham in order still more to exalt Melchisedec. When Christ is the subject, the singular "promise" is used. "The promises" in the plural, refer to God's promise of greatness to himself and his seed, and of the possession of Canaan, twice repeated before the blessing of Melchisedec. As the priests, though above the people (He 7:7) whom it was their duty to "bless," were yet subordinate to Abraham; and as Abraham was subordinate to Melchisedec, who blessed him, Melchisedec must be much above the Levitical priests.