Gravity can be used two distinct ways, but the word came from a single root.
The intention, was probably not use in two fold manner in two distinct contexts. At some point added connotation developed.
That is my hypothetical which I did not have time to research, as not even now, but may have time later.
A grave matter is a serious matter, as related to gravity, whereas a heavy object does possess the same, albeit
an effective reaction to a pulling force of gravity.
From Thesaurus: comes this:
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The word gravity comes from a Latin word that means “heavy.” Its first meaning in English was “seriousness and dignity.” It was first used as a scientific term for the force that causes objects to have weight in 1641.
The different contexts are separable , inducted through the passage of time , the meaning and use are not really separate in the sense of syntax but in the use of the word in different contexts.
The same meaning , ‘heavy’ pertains to both uses, for all uses stream from the same word. That the appear contextually different is also a misnomer, because as ’ heavy’ is applied into different uses, it bears the identical meaning.
How is that? The heaviness of anything can change the contextual quality, and not the other way around.
We can apply ‘grave’ to any intended association, thereby declaring it into as many effects as we are intent on doing. Some have become conventional meaning direct to the original Mean ing, others may become unconventional .
If I were to say that a flower had a certain gravity about it, as it hung sadly from lack of sunlight, such would appear totally discordant from ordinary conventional sense of the usage, but it will still retain the similarity to the word. The context need to have adapted the characteristic similar to the conventional one, where ‘grave’ is associated with a conscious solemnity. However such inconsistency will not negate the use from the definition of primary meaning.