The double-headed eagle happens to be one of the oldest Indo-European symbols. Its history is a mixture of Christianity, Paganism, Zoroastrianism, the epochs of great empires and those of feudal fragmentation.
The double-headed eagle found on a grave may be a masonic symbol, associated with Scottish Rite Masonry, or as a symbol of the Orthodox Church (in particular Greek Orthodox).
In the Orthodox Church, the double-headed eagle was the official emblem of the Christian Greco-Roman Empire as it developed after Emperor Constantine moved the centre of the Empire from Rome to the small town of Byzantium, which he renamed "New Rome". This "New Rome" (later known as Constantinople, City of Constantine) was now a Christian city, built again on seven hills, but centered around the Church of Ayia Sophia (Holy Wisdom, which is Christ). The Emperor was then able to return from his military expeditionswithout offering sacrifice to the goddess Victory, as every emperor before him had to when they returned to the old Rome. He embraced Christianity as the faith of the Roman Empire and initiated the process of the 1,000 year Christian Greco-Roman civilization, known today as the Byzantine Empire and Church.
The two heads and two sceptres of the eagle symbolize the two authorities, the Church and the State under one Crown, the Christian Empire - one Empire under God. The co-existence of the Church and State in "Symphonia", a period ofpeaceful co-existence and co-operation, where the Emperor made into laws the decisions of the Church Synods (especially those of the Ecumenical Councils), while the Church authorities respected the laws of the State. This formula of separation but close co-operation between Church and State worked quite well during the thousand-year-life of early Christian civilization. It enabled the Church to freely live the teachings of Christ and greatly affect the lives of people without having to resort to political and secular methods. In exchange for this freedom, the clergy refrained from political and secular endeavours.
Today, the double-headed eagle symbolizes the Christian Greco-Roman heritage - most especially the glory and civilization of the Christian Empire known today as the Byzantine Empire and Church.
From whence came this two-headed eagle, and how came it to be associated with Scottish Rite Masonry? The last part of this question is easier to answer than the first, for there is direct testimony that Frederick of Prussia supplied this crest during the formative stages of the Rite, but neither Frederick nor indeed Prussia could claim the exclusive right of its use or the ability to bestow it. It was the imperial emblem of Russia, Austria, Serbia and other portions of the disrupted Holy Roman Empire, and Prussia adopted the emblem long after it had flown over Byzantium as the royal arms of the "Emperors of the East and West."
The emblem soon spread throughout all Europe, an inheritance from the Knight Crusaders. In England we find it used on knightly arms. Robert George Gentleman displayed it upon his shield, with the motto, "Truth, Honour and Courtesy." In France we find it used by Count de Montamajeur, and associated with the motto, "I shall hold myself erect and not blink." We find it upon the arms of the Duke of Modena, (1628) with the legend, "No age can destroy it." It appears upon the shield of Swabia in 1551, in Russia in 1505, and as the crest of the city of Vienna in 1461.
Source:
The Builder - April 1923
www.masonicdictionary.com
http://www.stgeorge-newportrichey.org/Flags_and_Symbols/Church_Flags_Symbols.htm