For firearm cartridges, both the powder charge and bullet weight are measured in grains. Taking out the human factor - some barrels will be more accurate with lighter bullets while other barrels will be more accurate with heavier bullets. Taking the human factor into account, a heavier bullet will spend more time traveling down the barrel so the shooter theoretically has more time to complete the follow through. However, sometimes a heavier bullet may produce more felt recoil, and felt recoil can be a problem for some shooters. The increase in felt recoil from a cartridge with a heavier bullet is from the greater resistance of the heavier bullet not because there is more powder (should be less powder) for the load with a heavier bullet. For a shot to be accurate, the bullet needs to become stable during flight and stay stable until it hits its POA. Some elements of the equation to bullet stability are the rate of twist, bullet shape, bullet weight and speed of the bullet when it leaves the barrel.
If you are thinking about reloading, be sure to find a good mentor with a lot of actual experience. The NRA also has a reloading class that will teach you the basics. The chamber pressure of a cartridge needs to fall within a specific range (too low may have a squib which is a bullet stuck in the barrel - too high has potential to cause catastrophic damage to chamber, action, receiver, frame, barrel, shooter and spectators). Generally, if a heavier bullet is used less power is to be used. It is important to use reloading data from a respected company that is specific to the particular bullet weight, bullet manufacturer and model as not all bullets of the same weight have the same affect on the chamber pressure. You also need to use loading data specific to the powder. There are other critical aspects to reloading besides chamber pressure, so get proper training if you are considering loading your own ammo.
Those who do choose to load their own ammo are able to find a load that performs well in their firearm - if the firearm is not damaged and all other factors are done properly (stock fit, bedding, optics/sights, etc.). They can experiment and find the right power, powder charge, bullet weight, bullet manufacturer and model, etc. that works well or very well in their particular firearm.