As the main root for “two”, √AT dates all the way back to the Qenya Lexicon of the 1910s where ᴱ√ATA appeared with the gloss “dual” (QL/33). At this very early stage, its derivatives had mainly to do with pairs such as ᴱQ. aqi “a brace, a couple of, both” and at- “bi-, twi-”, whereas the earliest Quenya word for “two” was ᴱQ. yúyo (PE14/49). Later on, Q. yúyo became “both” whereas “two” became Q. atta.
In The Etymologies of the 1930s this root appeared as ᴹ√AT(AT) (Ety/AT(AT)) with variants ᴹ√ATTA which became the basis for Quenya atta “two” (Ety/ATTA) and ᴹ√TATA which became the basis for Noldorin tâd “two” (Ety/TATA); these numerals retained this form thereafter into the Quenya and Sindarin of the 1950s and 60s (VT42/24-26). In the 1930s, the ᴹ√TATA variant took on the sense “double” in Quenya, and the ᴹ√ATTA variant took on the sense “across” in Noldorin. The base root ᴹ√AT had the sense “again, back”, as seen in both Quenya and Noldorin prefixes ᴹQ. at(a)-, N. ad- “back, again, re-” (Ety/AT(AT)).
This root continued to appear in the 1950s and 1960s, retaining its various meanings of “two” (VT42/27), “back, again” (PE17/148) and “across” (VT43/33). Tolkien explored the origin and development of this root at some length in his essays on Elvish numerals from the late 1960s, connecting it to √AT(AR) “father” via various Elvish finger names (VT48/19).