Regarding the comparative size of the Arkenstone to a Silmaril, there is this from the Hobbit:
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His [Bilbo's] small hand would not close about it, for it was a large and heavy gem.
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Again, I realize there was a marked difference in size between Bilbo and Beren (who clutched a Silmaril in his closed fist), but it does give one pause to consider a size difference in the two gems. In addition, The Hobbit text states that the Arkenstone 'was cut and fashioned by the dwarves', meaning it was faceted and shaped from a larger raw stone. Would the dwarves ever consider cutting and fashioning a peerless gem such as a Silmaril? The dwarves of Nogrod refashioned the Nauglamir to fit the Silmaril, but they did not tamper with the gem itself (after all, who better than a dwarf to understand all the facets of such perfection?).