Lets figure out that FRE equation you provided.
If we assume a limited gun weighing 38 oz, 180gr bullet at 175pf, we get 4.237 ft/lb.
Add 3oz onto the weight of the gun, and we get 3.927 ft/lb. That's a ~7.5% decrease in kinetic energy. That's only for a free recoiling firearm. ie, one that isn't being held.
Yes, the lighter gun will have more kinetic energy after a given distance traveled than the heavy gun, in the same way the lighter can has more kinetic energy than the heavy can at the same height.
But you're there to hold the gun, so the energy is transferred into you instead. We're s