Here is a beautiful explanation by Fr. Tom Carzon:

The sacrament of baptism is the foundation for all the other sacraments of the Church. Stating that the marriage of a baptized and non-baptized person is non-sacramental is not a judgment of their love or conscience, nor does it say their relationship is somehow second-rate. It is taking seriously the fact that while one party lives an explicit life of faith rooted in baptism, the other party does not share that faith or baptism.

It would be a mistake for a man and woman to gloss over their own spirituality, or explicit lack thereof, in coming together as husband and wife. A sound and solid relationship is one built on truth, and the personal spirituality of the spouses is a very important truth to consider. Likewise, the Church wants to respect the truth of this man and this woman. 

One may perceive that the symbolism of marriage does not apply to a non-sacramental marriage. But that is not true. In fact, the reason marriage between baptized persons is considered a sacrament is precisely because of the deep meaning of marriage as a natural institution, part of the very pattern of creation.
Now, all the sacraments are sacraments of faith.  They are not magic or make believe. They presuppose faith in Jesus Christ as the Son of God - both on the part of the Church, the community where the sacraments are celebrated, and on the part of the individuals who devoutly receive the sacraments. For someone who does not have this faith in Jesus Christ to receive the sacraments would be merely external rituals without any inherent meaning.
As a sacrament, marriage symbolizes also the union of Christ and his Church. For a non-baptized person, or for someone who does not believe in Jesus Christ, this symbolism would be meaningless, or perhaps even offensive.

As a woman and man come together in marriage, they share everything they hold in common, yet they still remain unique individuals. It would be wrong for a believing spouse to force a non-believing spouse to practice a faith that they did not share. And it would be wrong for a non-believing spouse to forbid a believing spouse to practice the faith he or she does hold. 

Difference between grace and blessing

What is grace?

Grace is favor, the free and undeserved help that God gives us to respond to his call to become children of God, adoptive sons, partakers of the divine nature and of eternal life.

Grace is a participation in the life of God. It introduces us into the intimacy of Trinitarian life: by Baptism the Christian participates in the grace of Christ, the Head of his Body. As an "adopted son" he can henceforth call God "Father," in union with the only Son. He receives the life of the Spirit who breathes charity into him and who forms the Church.

This vocation to eternal life is supernatural. It depends entirely on God's gratuitous initiative, for he alone can reveal and give himself. It surpasses the power of human intellect and will, as that of every other creature

The grace of Christ is the gratuitous gift that God makes to us of his own life, infused by the Holy Spirit into our soul to heal it of sin and to sanctify it. It is the sanctifying or deifying grace received in Baptism. It is in us the source of the work of sanctification. CCC 1999

What is a blessing?

In a blessing, the Church calls God’s protection on the couple, asking God to sanctify and bless the pair and their marriage. The sacrament also includes a blessing.
Blessings are not sacraments; they are not of Divine institution; they do not confer sanctifying grace; and they do not produce their effects in virtue of the rite itself. They are sacramentals and, as such, they produce the following specific effects:

  1. Excitation of pious emotions and affections of the heart and, by means of these, remission of venial sin and of the temporal punishment due to it.
  2. Freedom from power of evil spirits;
  3. Various other benefits, temporal or spiritual.

Blessings express a wish or desire that all good fortune, especially of a spiritual or supernatural kind, may go with the person. A blessing signifies the sanctification or dedication of a person to some sacred purpose. 

A blessing may be described as a rite, consisting of a ceremony and prayers performed in the name and with the authority of the Church by a duly qualified minister, by which persons or things are sanctified as dedicated to Divine service, or by which certain marks of Divine favour are invoked upon them (emphasis added)