18 that by two immutable matters, in which it is impossible for God to lie, we may have a strong consolation, who are fleeing for refuge to lay hold of the expectation lying before us,
19 which we have as an anchor of the soul, both secure and confirmed, and entering into the interior beyond the curtain,
20 where the Forerunner, Jesus, entered for our sakes, becoming Chief Priest according to the order of Melchizedek for the eon.
1 For this Melchizedek, king of Salem, priest of God Most High, who meets with Abraham returning from the combat with the kings and blesses him,
2 to whom Abraham parts a tithe also, from all; being first, indeed, translated king of righteousness," yet thereupon king of Salem, also, which is "king of Peace";
3 fatherless, motherless, without a genealogy, having neither a beginning of days nor consummation of life, yet picturing the Son of God is remaining a priest to a finality.
4 Now, behold how eminent this one is to whom the patriarch Abraham gives a tithe also of the best of the booty.
5 And, indeed, those of the sons of Levi who obtain the priestly office have a direction to take tithes from the people according to the law, that is, their brethren even those who also have come out of the loins of Abraham.
6 Yet he who is not of their genealogy has tithed Abraham, and has blessed him who has the promises.
7 Now, beyond all contradiction, the inferior is blessed by the better. (Hebrews 6:18 - 7:7)

I am totally convinced that the Bible is here calling our tithe as much our expectation that goes beyond the veil, as it's saying Lord Jesus is our expectation that has gone beyond the veil.  This passage is as much calling our tithe to be without father, without mother, without genealogy, without beginning of days nor consummation of life as it's calling our redemption and our Redeemer, ultimately, those things as originating, in all actuality, in the Heart of God.  Our tithe pictures the Son of God, [according to the above Scripture,] and as Israel was first birthed through Abraham tithing to Melchezedec, I believe this is indicating that Israel will be born again through our practice of worship before Christ with our tithe. 

I believe this passage is calling our tithing a form of overcoming on par with Abraham having combated the ancient kings he engaged in warfare with.  As we tithe, in addition to inheriting a blessing, I believe this is indicating that we'll inherit Israel again.  This isn't to be confused with the Indulgences based system of the Catholics from yesteryear, but a form of spiritual warfare that keeps things in perspective that Lord Jesus is their Messiah, and tying this to Jesus's teachings, it's laying up the tithe as a treasure in heaven, so that as 1Timothy 6 and Philippians 4 says, we can lay hold on it.