So no, I wouldn't consider this supernatural.
this has been stated, but he was refering to sleep paralysis. it's a strange hybrid of waking and sleeping states. the hormone that keeps the body still during rem sleep (preventing movement acted in dreams, apparently) is on, while the concious mind is awake. the result is usually one of the most terrifying trips anyone will ever experience.
i have a friend that suffered from these for a while. i myself had one last week.
the "sitting on the chest" phenomenon is part of the paralyzed state. people often feel weight on their chest, like they can't breathe, or can't move. some people report the opposite, however, like they are being lifted off the bed. the figures are always "fuzzy." as in out of focus. sometimes waxy, almost. it's part of the concious mind not being able to fully resolve the dream state, or something. if you've ever seen "eternal sunshine of the spotless mind" they tend to look like the people in previously-erased bits. creepy. as. hell.
sometimes the figures are perceived by the dreamer as demonic, sometimes alien. this is definitally the origin of the incubus and succubus legends, and probably most alien abduction accounts. experiences are sometimes sexual. they are also always terrifying. something about the state seems to trigger some kind of chemical reaction in the brain that produces irrational fear. the fight or flight response, only you can't do either. these experiences are especially REAL as well, for two reasons. 1: it's rather tricky to know you're dreaming during the dream. 2: they happen where you feel asleep, and you are aware of your surroundings.
they tend to happen or happen more frequently when sleeping patterns are out of whack. falling asleep at weird times, in strange settings, or in the wrong clothing even.
when i had one last week, my first time really, i was able to subconciously recognize what was happening, and ignore the terrifying figure. i even made him go away, by concentrating on the cd player i had willed to play. i guess to distract me. then i gradually regained conciousness, and spent a good minute and half trying to figure out what happened to the next song on the cd, and how i'd been listening to it all considering it was in the car.
however, i do not suspect a person prior to the late 20th century would have been able to identify what was going on. they would not read it as a brain chemistry thing, but a religious matter such as the incubi and succubi accounts.