等 = ⺮ (bamboo) + 寺. It comes from bamboo writing-slips trimmed to EQUAL length and sorted by rank — so 等 first meant 'equal / grade / rank'. From 'taking your place in the ordered line' grew the everyday meaning: to WAIT.
等 has three faces. WAIT: 等你 (wait for you, with 你), 等一下 (wait a moment, with 一), 等等 (hold on). RANK/GRADE: 一等 (first class), 等级 (level). And 'etc.': a list ending in 等等 means 'and so on'. The most useful is 等 = wait: 请等一下 (please wait a moment) is everyday politeness. Patience built into a character — fitting for 知止.
Bamboo slips (⺮) sorted to equal rank — taking your place, to WAIT.
等等 means both 'wait a sec' and, at the end of a list, 'etc. / and so on'. The same 等 grades things into ranks: 一等 = first class.