I thought it was the inertia of the bolt, not the rest of the shotgun, that regulated the Benelli's cycling?
It's not clear to me how increasing the weight of the rest would affect anything - other than some O/U shotguns (in which the second barrel is set up to shoot by the recoil of the first) most semi-auto firearms are more likely to malfunction if allowed to recoil freely, rather than by meeting resistance, unless the moving parts are bound up somehow.
Because it's the bolt's
inertia to sit still for a split second while the rest of the shotgun recoils that works the Benelli mechanisim. The more the Benelli moves, the more reliable it is. Which is completely opposite from most all other gas-operated autos where letting the rifle/shotgun move too much, or recoil operated pistols (limp wristing) can rob momentum from the piston, slide, bolt, or other reciprocating components.
If the Benelli-style inertia-locked shotgun masses more, it moves less under recoil because it's own inertia is increased. Which is why side-saddles, optics, and tac-lights eventually reach the tipping point making a Benelli recoil-operated autoloader unreliable. An overly strong shooter with a very rigid hold and shoulder can also induce the same malfunction. Fixing the buttstock against something completely rigid like a telophone pole etc. would also induce a malfunction.
And since every shooter is different under recoil, and even different at the end vs. the beginning of a shooting day when they're tired out, it makes "how much is too much weight" on a Benelli a very dicey proposition.