Throw some paniers on a mtn bike, load it with 15lbs of stuff and climb a hill. Put on a back pack, load it with 15lbs of stuff and climb a hill
The bike itself should still accelerate and climb the same with the load on your body, not the bike. Essentially your bike goes from, as an example, 25 lbs to 40 lbs where your legs are trying to propel that 15 extra pounds beneath you instead of "carry" it on your upper body (which normally is going to be seated). 15 extra lbs on your upper body is nothing...
Granted, a heavy pack not properly secured to your torso/back would invite all kinds of problems...