From the New Testament texts... Galatians 6:18 "The grace of our Lord Jesus Christ be with your spirit, brethren. Amen" and 2 Timothy 4:22 "The Lord be with your spirit."
Fr. Joseph Jungman S. J. had two footnotes about the origin of this, one in which he called the phrase a Semitism that simply meant "and also with you" (which obviously is what the original ICEL translators focused on to arrive at the translation that we have been using over these past years). Yet another footnote alludes to the fact that this reply in the usage of the Church's liturgy was given only to a priest or bishop and that the implication was that the greeting was to the Holy Spirit that the ordained minister had received upon their ordination. St. John Chrysostom mentioned this in a homily and an early Council of the Church reinforced its meaning.
What saying "And With Your Spirit" can teach us...
The Liturgy is the work of the Holy Spirit, not the individual presider. In fact there is no "individuals" in the liturgy save the Body of Christ. Our response acknowledges the one Holy Spirit poured upon the presider and reminds us that the work we witness in this Eucharist is the Opus Dei...the work of God.