A 1 1/8oz charge is 28.6% heavier than a 7/8oz charge, Have absolutely no idea where the 2X factor comes from.
Just to muddy the waters a bit remember the entire travel of the load from a standing start to exit from the muzzle occurs in a bit less than 3/1,000 of a second. Take another look at the DuPont chart Drew posted, the part where the "Fast Powder" is exceeding the "Slow Powder" in its pressure rise is a mere fraction of that already minute fraction of total bbl time. The slower pressure rise of the slow powder is offset to a great extent by its heavier charge weight & the fact it maintains a bit higher pressure down the rest of the bbl. From the other thread on this subject I will add there are no cases where both Red Dot & Blue Dot are suitable for giving the same weigh of shot the same velocities. All powders suitable for shotshells are reasonably "FAST" in the lineup of propellant powders. Powders suitable for giving equal balistics to a given shot weight are not really that different in their burn rates. Some of the most dependable light recoiling loads in existance use fast powder, for the simple reason they will burn cleanly at reduced balistics with a light load of shot, something a Slow Powder cannot always be depended on to do.
Also don't be kidded that the acceleration of the gun exactly folloows the pressure curve, it follows the accleration of the velocity curve. Inertia plays a big part here which tends to smooth things out. Assume that the gun weight is 90 times that of the total ejecta weight, a reasonable number, then while the charge travels 30" (Yes I am aware you will likely never have that "Exact" amount of travel inside the bbl, but near to it) the gun will have traveled 1/3" It will have received the force to overcome its inertia in this short distance & the rest of its movement is After the shot has left the bbl.
For every person & for each gun there is a level they will be comfortable with. For a comfortable load take the total weight of everything that goes out the bbl (Shot, wads & powder). Multiply that by the muzzle velocity & divide by the guns weight. This will give you the recoil "Velocity" of the gun in FPS. Any load which falls within that limit will be comfortable to shoot, those which exceed it will grow increasingly uncomfortable the more they exceed it. The same level will not necessarily apply to a load for firing many rounds in a short time as for firing a few rounds over a more spread out time frame. The recoil velocity of a given gun for any individual though is the absolute most important factor in recoil, everything else is mostly advertizing "HYPE". Don't forget also in doing the calculations all weights have to be consistent, whether you convert it all to grains, ounces or pounds is immaterial as long as you make them all the same.
As an example if you used an ounce of shot, 35 grs of wadding & 20 grains of powder & fired them from a 6lb gun & acheived 1200fps M Velocity you would get a recoil velocity of 14fps. Most people would find this reasonablly comfrotable except for concentrated firing of many rounds.
A phenomenum here is that changing the recoil velocity nearly always has a more pronounced effect than a change of recoil energy. If you increased the load to the point it would produce that same 14fpc R Velocity in an 8lb gun then the R Energy would be increased by 33%, however most people would still find it reasonably comfortable. This would represent recoil energies of about 18 & 24 units of kinetic energy for the 6lb & 8lb guns respectfully. "IF" on the other hand you increased the load in the 6lb gun to the point it acheived that same 24 units of kinetic energy it would seem much more uncomfortable.
