Except… none of these words actually have -gress in them. They’re all from ghredh-, though, which is the Proto Indo European origin of the -gress words. Now, we already did -grade words, which includes upgrade and degrade, but there are still plenty of others for us to look at.
Degree showed up in the thirteenth century meaning a step or stair (makes sense), a stage of progress/single movement towards the end (still makes sense) or a position in a hierarchy (uh, less sense). It comes from the Old French degré, which had the same meanings as above as well as an academic degree (maybe that’s related to the hierarchy thing?), so that explains where we got that from. Kind of. It’s from the Vulgar Latin degradus, a step, a mix of the classical Latin de-, down, and gradus, which means a step or a degree. Yeah, a bit recursive there. And gradus of course is from ghredh-, the word that unites these all together.
Graduate showed up in the early fifteenth century and fun fact it used to be “graduate man” before just graduate the sexist bastards. It’s from the Medieval Latin graduatus, past participle of graduari, to take a degree. And that’s from gradus, which means degree. A degree is something that signifies “a degree of something rising by stages”, and that’s why graduates have degrees.
It shouldn’t surprise anyone that gradual is part of this family. It showed up in the early fifteenth century meaning having steps or ridges, from the Medieval Latin gradualis, which is from gradus. Wow, these are getting shorter and shorter. Anyway, something gradual is taking place by degrees, so a graduate gradually graduates with a degree.
Yes, this word belongs here, too! And once upon a time it was sometimes written as engredient. It also showed up in the early fifteenth century, coming from the classical Latin ingredientem, which can mean things like “that which enters into” something, like an ingredient to a recipe. It’s the present participle of ingredi, go in or enter, a mix of in-, which is from en and means in, and gradi, to step. An ingredient is something that steps in.