Generally when lighter bullets are used there is more surplus airspace or "case capacity" in the cartridge compared to the same case loaded with a heavier slug. There are exceptions, the best known being the Barnes X-bullet. Those excellent, all-copper projectiles are rather long for their weight compared to conventional bullets with lead cores. So they take up slightly more case capacity than a same-weight bullet with a lead core. Bullet weight and length are the two main reasons why you can put more powder into a .30-06 loaded with 150's than you can the same cartridge loaded with 180's, for example.
Another factor is the way smokeless powder burns. Put a match to a small pile in the open and it takes several seconds to burn. Compare that to the one or two thousanths of a second when it's under pressure in a gun barrel. The more pressure, the faster it burns and the faster it burn the more pressure it creates. Now since the lighter bullet is easier to accelerate, we can use more powder to keep the pressure up. Or we can use a faster burning powder.
One of the "givens" in the equation you asked about is the strength of the firearm. As you know - each type of action has been rated to withstand a specific amount of pressure.
With all other things constant in a load - increasing the weight of the bullet increases the pressure; decreasing the weight of the bullet reduces pressure. Less mass equals less resistance to bullet movement in the bore. As the powder burns and begins to build the pressure that forces the bullet down the bore - the lighter bullet will begin to move more easily than a heavier bullet.
If we load to keep pressure constant - a larger powder charge is needed to reach a given pressure with the light bullet than for the heavy bullet.
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