I'm not much of a 12ga person and the ones I do have are all 2 frame guns with 30 or 32 inch barrels so they aren't much help but here is a comparison of two guns both O frames with 30 inch Damascus barrels.
GHE 16 total gun weight is just shy of 7.5 lbs. Unstruck barrel weight 3.1 lbs.
GH 20 total gun weight 6.5 lbs., unstruck barrel weight 3.6 lbs. There is only a half pound difference in barrel weight between these two guns but a pound in overall weight.
I think the majority of the difference in weight is the combination of factors such as stock configuration,splinter vs BTF, straight grip or pistol grip, Skelton butt or pad. Ejectors will add a small amount of weight as well. Wood density also comes into play.
The GHE is a straight stock, skeleton butt and BTF. The GH is a pistol grip, splinter forearm and factory butt plate.
The 16 weighs a half pound more than your 12 and the 20 is a half pound less.
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There is no hunting like the hunting of man, and those who have hunted armed men long enough and liked it, never care for anything else thereafter...Earnest Hemingway
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