Well I will defer to some one who might have a good idea on how to build a Double.
Holland & Holland list the following weight guide
.300 H&H 8lb 10oz
.375 H&H 9lb 6oz
.500/465 H&H 10lb 2oz
They also list the following built guns for sale
.470 10lb 11oz
.375 Flanged 10lb 2oz
.300 11lb
.300 9lb 14 oz
.577 15 lb
I might add that I have a 458 lott built on a Sako action that weighs 8.65 pounds with scope and NEEDS WEIGHT. I also have a CZ Lott at 9.4 with out scope not to bad but still light perhaps a heavey scope might help. My Kimber .375 weighs in at 9.3 with scope.
Bill