Aware, and aware of being aware. Its root is knowing-with — the Latin says two parties share what is known.
Latin conscius (knowing, aware), from com- (together, with) + scire (to know); knowing WITH — the root names a shared knowing, not a solitary awareness.
Aware, and aware of being aware. The root does not describe a private state; it describes knowledge held with another, which the modern sense keeps as an echo.