If it were me looking for a sympathetic repair, Bazlye's suggestion (post 3), is surely the best. Not necessary to make a hole saw, they can be bought rather cheaply, like this Makita set on Amazon.
Drilling a cored hole leaves the exterior of the weight in authentic aged condition. It doesn't matter how much damage is done removing the core, perhaps with a chisel, because it will be refilled with lead (most of it original!). The eye can be re-fixed in the original way too, by thrusting the end deep into the molten lead so it's firmly gripped when the lead solidifies. Not difficult to melt lead with a DIY store blow-lamp and a small steel pan.
Dave