You asked:
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1) What's the difference between these two expressions ("most heavy"; vs. "heaviest"?
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Answer: "most heavy" is grammatically incorrect; whereas "heaviest" is the grammatically correct superlative form of "heavy". The grammatically correct comparative form of "heavy" is "heavier".
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2) Which one is grammatically correct?
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"Heaviest" is the grammatically correct version, in the superlative form; and "heavier is the grammatically correct version, in the comparative form.
"Most heavy"—or "more heavy—do not exist! (and are grammatically incorrect!).
