Where the shape comes from
An adze: the blade at the top and the handle bending away below it. It marks cutting and splitting — 新 was fresh wood cut with an axe, and 断 is something severed — and it lends its sound to 近 and to the simplified 听. The weight sense is a separate borrowing, but a live one: fruit is still sold 一斤 at a time.
汉字 filed under 斤
No published character on HSK Guide is filed under this radical yet. 汉字库.