Steep & stoop
It seems reasonable that these words might come from the same root:
steep the tea
hang out on the stoop
However, only three of them share a root.
The verb steep (to soak in liquid) made its way into English in the early 1300s. Though nobody is certain of its source, it may have come from a Norse word meaning to pour.
The noun stoop (raised platform at the front or back of a house or apartment), appeared in English in 1755 from a Dutch word meaning a flight of steps.
The three words that share a source are the verb stoop, the adjective steep, & the noun steeple. They all come from a Proto-Indo-European word meaning to push or knock. A version of this root made its way into northern European languages meaning to bow or bend, & then into Old English as the verb stoop. Another form of this root came to mean high & lofty (possibly due to the idea that a mountain is pushed up from the surrounding soil). This form of the root found itself becoming both the adjective steep & the noun steeple.
It nearly causes one to want to stoop to steep one’s tea on one’s stoop, then climb up to enjoy the tea atop a steep steeple, eh?