Really it's not weight, but inertia. The greater inertia of a heavier gun resists being moved by recoil. If the gun weighed 100 pounds, it might feel heavy enough to hold, but you probably couldn't even feel any recoil at all when fired, regardless of how you hold it.
And, munk is right about stock design and such. Getting a gun to fit you can easily make a much bigger difference in felt/percieved recoil than whether it's a 16, 12, or 10 gauge. Like I said, my sister's 20 gauge is more painful for me to shoot than dad's 10 gauge.
And as far as waterfowling, the 3 1/2" 12 gauge was developed mainly in response to steel shot laws. Because steel shot is less dense than lead, we needed bigger pellets to carry the same distance. And because the pellets were bigger, we couldn't fit as many in a standard hull, which reduced pattern density. But, now we have Hevi-Shot, tungsten, and even newer versions of Hevi-Shot that are more uniform and even heavier than lead. So now I see less of a reason to go with the big shells, when a 3" Hevi-Shot round can basically give you the same performance as a 3 1/2" steel round. Yeah, these shells are extremely expensive, but if you're only talking about firing half a box per year, it ain't too bad. If you want to get serious about waterfowling and are gonna burn a couple hundred rounds every month, then maybe I'd look to the bigger shells with steel shot to save cost.
And of course as you know, your skill will make a far bigger difference in success than slight differences in the gun you're holding. For me, it really don't matter at all whether I go duck hunting with an automatic 10 gauge or a single shot .410. I can miss with 'em all equally!
