to climb there (Technically, it can mean "to climb there", but "hinklettern" would be more idiomatic in these contexts. )
Opposite (closest): hersteigen
The core idea of this root was:
walking, striding upward
The most notable English relative is the noun stair, but the root is also the origin of stickler, which originally was about putting on a base, and hemistich and stoichiometry. Which are both words I had no clue about. The first one has something to do with poetry and the second one with chemistry, bit the common theme is “layering rows“. Kind of like stairs :).
In German, steigen and its relatives are the only members I could find.