My mom's prayers were the real reason I returned to the Catholic Church, but now the question The Anchoress is asking is why do I stay Catholic? Because Christ has a body.
Don't you mean had? True, at the Annunciation Mary's humble willingness to accept what the angel Gabriel told her of God's plan for her was fulfilled in the incarnation of Jesus in her womb. He grew up with Mary and Joseph and, even in that mysterious time he stayed behind in the Temple when he was 12 to be in his Father's house, was obedient to them. He would go on to teach about the Kingdom of God, to suffer, to die, to be buried, and to rise from the dead. All this could do because he had a body. Even now, risen and ascended, he still has a body, one made fit to live eternal life.
And he has another body, the Church. He established the Church during his mission among us. He gave it his own authority to continue that mission, to build the kingdom of God. Everything that the Church is flows from the Incarnation. She, for the Church is also his bride as well as his body, she continues Jesus' Incarnation in time while he continues in eternity. The Church lives out Jesus' life, especially as she suffers and dies with him (Col 1:24). Christ and his Church will be united in what St. John in Revelation calls "the wedding feast of the lamb" (Rev 19:9).
The Catholic Church has sacraments because God uses matter to bring grace into the world, just like he bought his divine Son into the world in a human body conceived and carried in Mary. We have the Bible because the Word became flesh and gave us some of his words to be remembered. Catholic theology flows from the Church's understanding of the Incarnation--God in a Body.