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Since portals aren't real, maybe we can start from what we see in game: Chell can hold it for long periods of time without problem, so that puts an upper weight barrier on it. Aperture must've figured out a way to fit portal technology into it, or found a way to stash its mass away. Or maybe it's heavier than average, but Chell is drugged to be able to hold it.
There's no power cord in-game, so its energy source must be self-contained, because I don't think it can get enough power by absorbing things in the air.
I think you meant Aperture
thanks! I've fixed it.