PS

*twy - to eat, swallow (?) (Kogan 2015: 539)

Goes back to Afroasiatic *twy (HSED No. 2343).

Proto-MSA
*twy - to eat (Kogan 2015: 31)

With no evident Semitic etymology (for the rather sparse Akkadian comparanda see Kogan 2015:539). 

Akkadian
taˀû - to eat, to graze (CAD T 301, AHw. 1340)
Very poorly attested.
Akkadian
tiˀīum - food (CAD T 398, AHw. 1363)
Akkadian
tiˀûtu - food, sustenance (CAD T 439, AHw. 1363)