First showed up in the early fifteenth century from the Middle French assister (same meaning) and from there, the classical Latin assistere (stand by or attend). The prefix a- is short for ad-, which means to, while –sistere means “take a stand”. Sistere can be traced all the way to the Proto Indo European sta-, to stand, which was reduplicated (basically, they repeated the syllable to make it a new word form) into siste-.
First showed up in the late fourteenth century from the Old French resister and classical Latin resistere, which meant resist or withstand. The prefix re- means against and the –sist comes from sistere, take a stand, making it “stand against”.
This didn’t show up until the early sixteenth century, coming from the Middle French consister and classical Latin consistere, stand firm or stop. The con- comes from the prefix con-, which means together, and -sistere means stand as in to place something. This makes the word something like “placed together”. It makes more sense if you think of something being made of things placed together.
Showed up in the late sixteenth century from the classical Latin insistere, which means dwell upon. The in- means upon in this case and of course sistere is take a stand. When you take a stand upon something, you insist on it, right?
Showed up in the mid sixteenth century from the Middle French persisterand classical Latin persistere, which means something like to continue steadfastly. Per- means thoroughly, making the word “to take a stand thoroughly”. Kind of wacky, but it makes sense. If you do something thoroughly, you don’t give up—you persist.
Showed up in the mid fifteenth century from the Middle French désisterand classical Latin desistere, to cease or stand aside. Since de- means off, there’s no huge mystery with this one.
First showed up in the mid sixteenth century from the classical Latin (all together now) subsistere, stand firm. The sub- means under, making the word something like “stand under”, at least literally. I think we can all agree this word’s meant to be taken figuratively.
Yes, this word really is part of the –sist family. Exist didn’t show up until the beginning of the seventeenth century, although existence was around more than two centuries earlier. It came from the classical Latin existere—which is also spelled exsistere—and literally means stand forth and figuratively means exist. The ex- means out or forth, so that explains that. Well, mostly.
Transistor is the newest of the -sist words, not showing up until 1948 when it meant an electronic device. It’s actually a mix of transfer and resistor, which I guess makes one of its grandparents the Latin sistere.