Superman's Powers
Super strength: Superman isn't really super strong, the advanced telekinetic powers that all Kryptonians have while under a yellow sun allow him to partially relieve some of the weight of the object. Also, the heightened gravity the beings on Krypton experienced would mean that the entire race of people that Superman belongs to would also be able to lift cars to warm up.
Flight: This to goes along with the telekinetic powers theory. This theory isn't complete, however, because Superman is most likely heavier than some of the things he lifts. But because Superman's body is part of what his mind wants to lift, the power becomes stronger/he can lift himself.
Super Speed: Again, Krypton's higher gravity means that its inhabitants need stronger legs. When that strength is no longer needed to walk normally on Earth, Superman's legs allow him to run really, really fast.
Vision Powers All of Superman's vision powers are attributed to the thickness of Krypton's atmosphere, filled with dense, opaque gasses, causing it's inhabitants to develop eyes that are stronger that those of Earthlings.
Super hearing: The thick atmosphere of Krypton made it harder for sound waves to travel, to adapt, Kryptonians evolved super strong ears.
Super Breath: Yet again, the harsher conditions of Krypton bring about this power. The lesser amount of Oxygen means that Kryptonians need to take larger breaths to get the required amount. Their lungs are also larger than those of the average Earthling to allow for this. The much warmer atmosphere of Krypton caused Kryptonians to secrete a chemical in their wind pipes that cools the air to a much more breathable temperature.
.:. Weakness to Kryptonite .:.
Kryptonite collectively is bits of the exploded planet Krypton made radioactive by the Planets' destruction. The radioactivity mimics in effect the red sun of Krypton, which renders Superman's powers useless. Possibly by recreating 'near Kryptonian' conditions in the surrounding area, causing Superman's powers to be ordinary, as he needs them to even receive Earth-like sensory inputs. Humans may be oblivious to its effects.
.:. Weakness to Lead .:.
Lead one of the densest elements known to man. (And probably Supermen((little nerd joke there))) Lead blocks the harmful effects of radiation, like what is given off by X-ray machines (at least, that's what our dentist uses to protect us from the X-ray machine) Superman has X-ray vision. Obviously, that doesn't work.
.:. Benefits of Lead .:.
Lead also blocks the harmful effects that Kryptonite has on Superman. This leads one to believe that Kryptonite's radiation is X-ray in origin.
Please note that I do not own Superman, and I'm not affiliated with DC Comics in anyway. This theory is fan made, so I wouldn't take it seriously in anyway