I couldn't find many references to the size of the Arkenstone, but it did manage to fit in Bilbo's deepest pockets. Also, it is said that
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His small hand would not close about it
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This makes the Arkenstone seem quite big, in terms of jewels, even if hobbit hands are quite small.
Considering that the Silmaril could be set in the Nauglamir, it sounds as though the Arkenstone was probably larger. I don't see a stone in a necklace being of such a size that a hand couldn't close around it.