You can picture something holding itself up with nothing leaning in from outside — no post beside it, no hand under it, no money coming in from anyone else. The whole word turns on support, and support does two jobs in English: it holds a weight, and it pays the bills. Take away the outside help in either job, and you have self-supporting.
From self- plus supporting, as the source entry records. The two modern senses follow the two jobs the word support already does.
來源條目記的構成是 self-（自己）加上 supporting。現代的兩個意思，正好對應 support 本來就在做的兩份工作：撐住重量，和負擔開銷。
Wiktionary etymology note supplied in this packet (source_ref kaikki:3f6f69a190036ae4:1495876913:4861), "From self- + supporting"
Two branches
錢上撐得住
這一支把「撐住」用在開銷上：收入夠付自己的成本，不必有人在外面補。
adjective · B2
Able to earn enough money to pay for everything you need, without help from anyone else. It is used about people, and also about a business, a group or a project that brings in enough to cover its own costs.
自給自足的；能自負盈虧的
結構上站得住
這一支是最字面的那種撐：物體自己扛住自己的重量，旁邊不需要任何東西幫忙。
adjective · C1
Able to stand up or stay in place on its own, without posts, wires, a wall or anything else holding it up.
不靠支撐就站得住的