You reach out for the thing and your hand closes on nothing. There is no matter there: nothing to hold, nothing to weigh. Put that hand on a set of scales instead and the needle does not move — and that is where the second use begins, with something that adds no weight to the question being decided.
From Latin im- (not) plus materialis, from materia (matter, material), through Medieval Latin immaterialis and Middle French immateriel. The literal reading, not made of matter, is the older one; the source marks the not-important uses as figurative.
拆開來是 im-（不）加上 material（物質的）。material 來自拉丁文 māteria（物質、材料），再經 immāteriālis 和中古法文 immateriel 進入英文。字面的「沒有物質」是比較早的一層；我們手上的資料把「不重要」那幾個意思標成 figurative（比喻用法），所以兩者的先後關係是有出處的，不是我們自己推的。
Wiktionary entry for immaterial (kaikki extract supplied in this packet): from Medieval Latin immaterialis, from Latin im- + materialis, from materia; the unimportance senses are tagged figurative.
From the picture
秤不出份量：在這件事裡不算數
這一家把「沒有重量」從實體搬到判斷上。一件事放進這次的決定裡，指針卻不動，那它就進不了討論。要注意的是：它不是說那件事沒有價值，只是說它在這裡不影響結果——換個場合可能就很重要了。這是教學上的連結，資料也把這幾個意思標成比喻用法。
adjective · C1
Not important to the question being dealt with, because it makes no difference to the decision or to the result.
無關緊要
adjective · C1
Having no physical body and no physical form: made of no matter at all, so it cannot be touched, weighed, or held.
沒有形體的