Picture air being pushed through a tube that has become too narrow. It cannot move freely, so instead of a quiet breath you get a thin, high, whistling squeak that people can hear from across the room. That squeezed whistle is what wheeze names. Everything that follows keeps the squeeze: the noise itself gets the same name, machines that push air and are struggling are said to do it too, and someone laughing so hard that their breath comes out in little squeaks is wheezing as well.
From the word’s history
Wiktionary traces wheeze to Middle English whesen, perhaps from Old Norse hvæsa 'to hiss', and ultimately to a Proto-Indo-European root meaning 'to pant'. Both of those older meanings are about the noise breath makes rather than about breathing itself, which is still where the modern word puts its weight.
根據 Wiktionary，wheeze 來自中古英文 whesen，可能再接到古北歐語 hvæsa「發出嘶嘶聲」，更早的印歐語詞根意思是「喘」。這兩個更早的意思，重點都放在呼吸「發出的聲音」，而不是呼吸這個動作本身。今天的 wheeze 也還是這樣：它講的是聲音。
Wiktionary etymology text supplied in this evidence packet (source_ref kaikki:3f6f69a190036ae4:673166834, entry 'wheeze' verb)
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