The sense of "derives" from the Aramaic meaning of zayin זין as "arms". Klein says that meaning is probably borrowed from the Avestic zaena.
According to Klein the root זון - to feed - is not related. He claims it derives from the Akkadian zananu - "to feed". This is the root of the words mazon מזון - food and tezuna תזונה - nutrition. Steinberg, however, points out that there are many examples in Semitic languages where the same root refers to both war and food: זן, לחם, טרף , צידה (we've discussed the lechem connection here.) If we say that the letter zayin was originally a hoe, then we can see how a tool like that could be used (or reformed to use) as a tool of war.
There are a few other apparently unrelated words with the same root:
The root זין also can mean "to adorn, ornament". Klein writes that it is borrowed from the Arabic zana, zayyana, meaning "he adorned, decorated". The root זנה - "to be a harlot" is also not connected (more on that root here).
Zan זן meaning "sort, kind" is, according to Klein, borrowed from the Old Persian zana. There is debate about the word miznon (or maznon) מזנון - meaning cupboard, or cafeteria. Klein writes:
Most scholars - on the basis of Rav Hai Gaon's derivation - connect it with זן (= kind). Others suggest to see in it a loan word from Gk. mazonoios ( = a wooden trencher for serving barley). Greek mazonomos is compounded of maza (= barley meal) and nomos, from the stem nemaen (= to deal out, attribute).
The letter zayin alternates with tzade and samech: עלז/עלץ/עלס and with dalet and tet: זבח/דבח/טבח.