One idea runs through this family: to feed, to give what sustains. It is a hollow root (the middle letter is a vowel ו), so the verbs look short, לָזוּן, לְהָזִין, but the meaning is full: nourish, be nourished, sustain. From that core grow מָזוֹן (food) and תְּזוּנָה (nutrition), and a quietly modern twist: in computing, לְהָזִין means to feed in data, and הֲזָנָה is the input, the feed. Even the מִזְנוֹן, the canteen, is just the place where feeding happens. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Because the root is hollow (middle ו), the binyanim contract: pa'al לָזוּן and hif'il לְהָזִין keep no separate middle vowel slot. Pa'al is now mostly literary; the everyday verb is the hif'il לְהָזִין, which carries both the old sense (to sustain) and the computer-age sense (to feed in input). Pi'el, pu'al and huf'al are not lexicalized here.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.