The first problem you've got is that bullet velocity isn't determined by peak pressure. It's determined by average pressure on the bullet base during its whole trip down the bore. That, in turn, varies with the powder burning characteristics which are affected by bullet weight. That's because a lighter bullet accelerates more easily, offering less inertial resistance for the powder to build pressure against. In effect it offers less confinement because its fast forward motion expands the powder burning space more rapidly than a heavier bullet will.
The above is why, in order to reach the same peak pressure with a lighter bullet, you have to add more powder than was needed to reach that same peak pressure with a heavier one. More powder has more energy content and makes more gas. For that reason, pressure doesn't drop as far by the time the bullet gets to the muzzle, thus you'd expect it to raise the average pressure at the base of the lighter bullet compared to what a heavier bullet will see if loaded to the same peak pressure value with the same powder. That just the start of it mucking up the simple calculation. This is further complicated by opposing influences. One is the faster bullet causing the powder to expend more energy accelerating its own mass (chasing the bullet), so the pressure gradient from breech to bullet base increases. That makes the portion of the powder blown forward with the bullet burn more slowly than the powder at the breech if it gets lit at all. (Go look at the ground in front of firing points at a range sometime and see all the unburned powder grains out there). But the main factpr is the faster bullet spends less time in the barrel, making it a lot harder for the powder to make all its gas before the bullet is gone. For that reason ballistic efficiency can plummet.
I don't have a black powder example, but if you load a 24" barrel .223 Rem. with IMR 4895 to 54,000 psi under a 77 grain MatchKing, ballistic efficiency (the percent stored energy in the powder that is converted to kinetic energy in the bullet) is about 30.1% and ME is 1410 ft-lbs (these numbers from QuickLOAD). But if you load a 40 grain Hornady V-max to 54,000 psi with the same powder (assuming you can compress enough into the case to do the job), ballistic efficiency drops to 21.7% and you only get enough velocity for 1239 ft-lbs of muzzle energy. It's about a 12% loss.
"First contemplation of the problems of Interior Ballistics gives the impression that they should yield rather easily to relatively simple methods of analysis. Further study shows the subject to be of almost unbelievable complexity." Homer Powley
