Why do Christians stand when we sing?
Because the day of the Lord is consecrated to the Resurrection, it is a kind of image of our hope in the Resurrection, the attitude of standing had for the early Christians an eschatological meaning: it was considered the proper attitude for those awaiting with confidence the Parousia. So we sing while we stand!
Singing the Psalms while standing was a monastic tradition started by St. Benedict in the 6th century.
Standing. In modern times kneeling has become generally accepted as the most appropriate attitude for prayer. In antiquity, however, and for many centuries in the Church, standing was considered to be the most normal posture, and it is still so considered by the liturgy, except for times and ceremonies that call for a special expression of penance and humble adoration. Even today many of the older basilicas do not have pews or kneelers. Standing was considered by the Jews as the most fitting attitude in praying to the Lord (Ex 33.8, 10; Sir 50.12–13; 1 Sm 1.26; Ps 135.2; Mt 6.5; Mk 11.25; Lk 18.11) and in listening to Him speak (Ex 19.17; Neh 8.5). That the early Christians adopted this custom as the normal attitude for prayer is evident not only from the many images of the "orante" in the catacombs and on ancient sarcophagi, but also from the testimony of early ecclesiastical writers: Justin (Apologia 1.67; J. Quasten, ed., Monumenta eucharista et liturgica vetustissima 19), Tertullian (De corona militis 3; Patrologia Latina, ed. J. P. Migne, 2:99), and Cyprian (De dominica oratione 31; Corpus scriptorum ecclesiasticorum latinorum 3.1:289). St. Benedict made standing the official posture for chanting the psalms.
For the early Christians, as for the pagans and the Jews, standing was a natural expression of respect and reverence. But for the Christians, as is evident in the writings of the Fathers, it had the added significance of the new dignity, the liberty of the children of God, the freedom from slavery and sin through Baptism and participation in the Resurrection, which makes it possible to stand confidently before God with eyes and arms uplifted to Him. As the Second Eucharistic Prayer of the Roman Rite puts it: "We thank you for counting us worthy to stand before you and serve you." For Tertullian (De oratione 23; Patrologia Latina 1:1191) kneeling was a sign of atonement and penance, whereas standing signified joy, and for this reason standing was customary throughout the Easter and Pentecost season; it was contrary to Church discipline to kneel on Sundays (De corona militis 3; Patrologia Latina 2:99). As a matter of fact, the first Council of nicaea explicitly made standing obligatory on Sundays and during the Easter season (c.20; J. D. Mansi, Sacrorum Conciliorum nova et amplissima collectio 2:719–20). Something of this prescription still exists in the custom of standing for the Angelus on Saturday evening and throughout Sunday, and also for the regina caeli during paschal time. Because the day consecrated to the Resurrection is a kind of image of the future world, the attitude of standing had for the early Christians an eschatological meaning: it was considered the proper attitude for those awaiting with confidence the Parousia. In a very special way, standing was considered proper for the exercise of the priesthood. - Liturgical Gestures
There seems to be very little biblical support for standing while singing. It nevertheless is a way for us to incorporate our bodily actions to work in union with our whole being when praying or honouring the the Lord. It seems to be more an ancient tradition in many denominations rather than based on clear biblical support.
A posture for various parts of the Eucharistic liturgy and the Divine Office. Since different countries have different customs, the episcopal conferences have given corresponding directives to the people. From time immemorial, however, standing has been customary during the reading of the Gospel and the recitation or singing of the Creed, the Preface, and Sanctus.
Standing in itself is a very very ancient practice while praying. There are several biblical passages about singing in the Scriptures, but the physical position taken while singing is conspicuously missing. Seems God leaves that to us!
“Speaking to one another with psalms, hymns, and songs from the Spirit. Sing and make music from your heart to the Lord” (Ephesians 5:19).
One commonly known position for praying dating back to antiquity is the Orans. Even in modern times Catholic priests sing the Our Father at Mass while in this standing position.
Orans, a loanword from Medieval Latin ōrāns translated as one who is praying or pleading, also orant or orante, is a posture or bodily attitude of prayer, usually standing, with the elbows close to the sides of the body and with the hands outstretched sideways, palms up. It was common in early Christianity and can frequently be seen in early Christian art. In modern times, the orans position is still preserved within parts of the Catholic, Orthodox, Anglican and Lutheran liturgies, Pentecostal and charismatic worship, and the ascetical practices of some religious groups.
The orans posture was practiced by both pagans and Jews before it was adopted by the earliest Christians. Christians saw the position as representing the posture of Christ on the Cross; therefore, it was the favorite of early Christians. Until the ninth century, the posture was sometimes adopted by entire congregations while celebrating the Eucharist. By the twelfth century, however, the joining of hands began to replace the orans posture as the preferred position for prayer. It continued to be used at certain points in the liturgies of the Catholic and Orthodox Churches. In the Catholic Mass, it occurs at the orations, the Canon, and the Lord's Prayer.
In the twentieth century, the orans posture experienced a revival as a result of its widespread use within Pentecostalism and Charismatic Christianity. Often associated with contemporary worship, the orans posture is once again becoming a common gesture of worship among many Christian groups.
An early Christian painting of Noah in the gesture of orant.
Psalm 134 reinforces the orant position of praying while standing.
134 Behold, bless ye the Lord, all ye servants of the Lord, which by night stand in the house of the Lord.
2 Lift up your hands in the sanctuary, and bless the Lord.
3 The Lord that made heaven and earth bless thee out of Zion. - Psalm 134
Psalm 95:2 almost make it feel as if standing while we sing was most appropriate without actually saying it.
2 Let us come before him with a song of praise,
joyfully sing out our psalms.
3 For the Lord is the great God,
the great king over all gods,
4 Whose hand holds the depths of the earth;
who owns the tops of the mountains. - Psalm 92: 5
Even St. Paul encourages us to sing.
Speaking to one another with psalms, hymns, and songs from the Spirit. Sing and make music from your heart to the Lord. - Ephesians 5:19