You asked
Does sensor size affect low light?
Yes, it does. At the same framing and the same f-number, a bigger sensor collects more light in total, so images stay cleaner at high ISO. As a rough guide, full frame has about one stop of advantage over APS-C, and about two over Micro Four Thirds. That's the main reason I'd point low-light shooters toward full frame.
It isn't the whole story, though. Lenses and light matter at least as much. A fast prime like a 50mm f/1.8 gathers far more light than any kit zoom, whatever sensor it sits on. If you shoot mostly travel, street or hobby work, a good APS-C camera with good lenses will serve you well, and you'll carry it more. The full breakdown is in Sensor sizes, and for lens choices see Lenses.
Written by Claude from this site's pages.