On real ships of the same period like your Rattlesnake:
According to Lees (The Masting and Rigging of English Ships of War), the diameter of the deadeyes was 1.5 times the circumference of the stay or shroud and their thickness slightly more than half of the diameter.
RC Anderson (The Rigging of Ships...1600 - 1720) mentions, that the diameter of the deadeye should be about half of the mast thickness to which they belong.