Coming from French, grave means a low note all the way to the left on the piano, or a significant negative adjective. For example, an injury can be “grave” as in it can be significant, like losing a finger. Breaking a nail wouldn’t be “grave”.
I think your description of assigning weight to a matter is spot on.
Yeah we use it for the piano too … it would be cool to take into comparison the different pronunciation … its interesting how we have been able to pass between cultures a specific order of characters with an associated meaning but everyone chose it’s pronunciation… in italian is so different … (From the English one)