"With your spirit" was mentioned frequently at the end of the greetings by St Paul:

"May the grace of our Lord Jesus Christ be with your spirit, brothers and sisters. Amen" (Gal 6:18);

"The grace of the the Lord Jesus Christ be with your spirit (Phil 4:23);

"The Lord be with your spirit. Grace be with you" (2 Tim 4:22);

and

"The grace of the Lord Jesus Christ be with your spirit" (Philemon 1:25).

It seemed a bit confusing whether St Paul was referring to a human spirit or the Holy Spirit. The answer lies on what we have been blessed on baptism -- in the Name of the Father, and of the Son, and of the Holy Spirit. The church makes it clearer when it is included in our response because we are responding to our Priest who is acting in the Person of Christ and who is accompanied by the Holy Spirit.