This is not scientific, but merely an observation about payload weights and velocities. Over my lifetime shooting and hunting I have come to shun higher velocity loads. I'm not referring to those new hyper velocity loads that scream away at over 1300-1400 fps. Those are obviously high velocity, but I just don't care for anything much over 1200 fps anymore. At the same time, I have come to favor heavier payloads. Having spent a great deal of time shooting .410s up through 10 gauges, I find that I prefer the heavier payloads for the gauge . . . . 3/4 oz. in a .410, 3/4 oz. in a 28, 7/8 oz. in a 20, 1 oz. in a 16 and at least 1 1/8 in a 12. In short tens I really like 1 1/4 oz. However, these are not heavy recoiling loads at all in my guns. They're extremely pleasant to shoot because the velocity of most of my favorite loads is in the 1145-1175 fps range.
Heavier guns do not necessarily mean slow, cumbersome guns. Better makers learned long ago to construct their heavier pieces with dynamic handling characteristics. Pigeon guns have to handle like lightning but be able to comfortably utilize a heavy load (3 3/4 - 1 1/4 is the most common load). No one that has ever shot my 31 1/2" barreled Perazzi MX8 could believe it when I told them it weighs over 9 lbs. They can't "throw" a close rabbit target fast enough that I can't smoke it with that big gun. Don Amos' work from years ago with his turntable and measurements of M.O.I.(moment of inertia) opened my eyes to the subtleties of varying weights and types of shotgun's handling characteristics. It's just a personal observation again, but I think too much focus is placed on weight and too little on M.O.I.