I'm afraid this is another instance of Graves embellishing a myth with details which were not present in the sources he drew upon. In this particular case, it's not at all obvious why he would add the detail of Aegisthus being seven years old when he killed Atreus.
What is certain is that the age of Aegisthus is not mentioned at all in the two main sources we have for this myth (which are the only sources Graves cites in The Greek Myths), namely Fabulae 87 and 88 by Hyginus, and Apollodorus' Library (Epitome 2.14).
Even later, minor sources like Tzetzes' Chiliades, Lactantius' scholia on Tatius' Thebaid (4.306, in latin), and the First and Second Vatican Mythographers (in latin), make no mention of a seven-year-old Aegisthus at the time of Atreus' death.
Instead, the last three sources use the latin expression "cum adoleuisset" (="when he grew up") in reference to Aegisthus' murder of Atreus.
Similarly, this is how Robin Hard retells this part of the myth in The Routledge Handbook of Greek Mythology (a more academically oriented reference than Graves' The Greek Myths):
Some time
later, Agamemnon and Menelaos caught Thyestes at Delphi and brought him back to
Mycenae. Atreus threw him into prison and ordered Aigisthos (who was grown up by this
time) to kill him.
As to why Graves would add the detail of Aegisthus' young age in his retelling of this myth, I can think of a couple of reasons:
- it adds to the tradegy having a child, first attempt to kill his biological father, then witness the suicide of his own mother, and finally kill the man who raised him
- it makes more sense that a child would be manipulated first by Atreus and then by Thyestes into doing all of the above
- the very young age of Aegisthus might make more sense chronologically, considering that he was younger than both Agamemnon and Menelaus, and that both of them were still youths when they found refuge in Sicyon after Atreus' death
