Alien size growth

That works

This is accurate. The novel and original script answer a few things that were left unanswered in the final cut of the movie.

There was also a cut scene where they almost blast the alien out of an airlock, but Ash managed to sabotage it.

Yes, there is a scene in the novelization where the alien breaks into the food storage and rips metal boxes and canned food apart. The crew tries to kill it with flamethrowers, but the alien escapes into a vent.

And I guess since I mentioned flamethrowers, you scratch your head in confusion, and you are right to do so. The scene in question takes place after Brett's death. Meaning the food storage scene cannot be an explanation for the fast growth, because it takes place after it has already grown and killed Brett.

Foster tried to address it in the novelization indeed, but I think he failed miserably with this blunder.

And I don't mind! I can come up with fantastical explanations, if you really pressed me for it, but the very essence of the alien't rapid growth is that the crew's knowledge is miniscule about the alien's physiology. So every time they encounter the alien it has a surprise up its sleeve, and that's how the plot is constructed. The crew needs to feel - and us as well in the process - that the alien is - well - totally alien.

My explanation: while the alien was growing inside Kane, it not only fueled its growth into the cat sized chestburster, but it also created a "blob" of extremely dense nutrients (fat, proteins, etc.), and stored it inside its own body. When it burst out and got to a hiding place, it started growing, and consumed the blob, that provided the necessary nutrition for its growth into adult sized alien.

But again - this explanation is one of many I could come up with, and this one happens to try to respect the laws of biology and physics. It's a sci-fi movie, I could come up with more and more fantastical explanations, but hey - as I said they are totally unnecessary. Or better yet - come up with your own! You're watching a sci-fi, have some imagination then, don't expect everything to be neatly explained, especially if the centerpiece of the movie is an alien creature :-))

The idea of the Alien digesting and incorporating metal is great - The alien is obviously a very strange bit of biology. Alan Dean Foster didn't use it in the novelization, probably because he hadn't seen the actual alien as it would appear in the film in full detail. I would add your idea to the novelization/original script notion that the alien fed on stored food aboard the Nostromo.

Yes, but that takes place waaay after it has already grown in size.

The OP is about the size growth between chestbursting from Kane and killing Brett (where it appears as already grown).

Point being, lab-created or not, it has to get all that extra mass from SOME place.

The Hulk poses the same problem -- where does Banner's extra mass come from? But at least that's a comic book vs. hard sci-fi. (and they've explained it as gamma radiation turned into mass, which would take many nukes' worth of energy, and as mass that comes from a pocket dimension where I guess everything is green and angry)