yes pressure is essential for a controlled efficient burn.
let's take a look at H-110.
it's extremely fine grained and heavily burn deterrent coated.
if we removed the coating it's burn rate would speed up by probably double [or more] moving it down the scale to something like red-dot.
if we increased it's size, it would slow down again because there is more area to burn.
those are the tricks the engineers play to come up with 'new' powders without having to mess with the basic formula of the powder itself.
but since it is so small and so coated it needs to be pushing against something to generate the heat and pressure that keeps it in an efficient area.
drop the outside temperature and you affect the heat generation causing the powder to become unable to do the same thing over and over.
raise the outside temperature and you raise the minimum temperature the powder is able to maintain once again affecting the outcome of consistency [or over affecting it in some cases]
the heat and pressure allows the powder that is burning to transfer that heat and burn to the next granule much more efficiently.
if you don't have that you end up with partially burned pieces of powder unless the powder doesn't have the coating and can pass it along before the bullet is too far away.
that pressure might be 10,000 psi or it might be 60,000 psi.
it just depends on the coating and granule size.
as far as weight goes your accelerating the heavier projectile at a much slower speed, this retains a smaller volume the gas can occupy generating more heat and more pressure.
both things accelerate the efficient consumption of powder, too much of a fast powder and pressures sky rocket.
not enough of a too slow powder and nothing really happens because you never achieve the heat/pressure zone necessary to keep the powder going properly.
hit the balance of a slow enough consumption and enough powder consumption to maintain pressure and heat and your getting just about everything the package can deliver.
payload weight, powder efficiency, speed,, they all fall into line and are dependent on one another.
change one of them out and the balance is lost until something else is corrected to change the balance again.