The weight of the airplane has the predictable effect on performance.
If your C of G is too far forward, you may stall the elevator as you apply nose up control to raise the nose, particularly when heavy. Form the factory, GA planes are usually fairly safe from this. However, once a number of mods are installed (larger engine and amphibious floats, for example) the C of G can move forward (and the plane gets heavier too). I've had a few planes, which during testing were not adequately able to raise the nose to flare power off. One example was a 182 amphibian (search Youtube for "Rompene 2014"), which was right at the forward limit if you flew it solo. And, it ran out of up elevator in the flare, particularly on the water, where you want the nose really high. This was in part because of the mods on the airplane, and in part due to the installation of wing extensions and a STOL kit, but no corresponding changes to the tail to compensate for an increased pitching moment of the wing. The solution I developed was a vortex generator installation under the horizontal stabilizer which increased the effect of up elevator by preventing it stalling. That, and 50 pounds of ballast carried in the furthest back float compartments, and the plane flew well. The ballast was carries as tools, spares and emergency supplies to be useful. If used, they were to be replaced with rocks or such for the flight home.
If the C of G is too far aft, the effect of the natural [designed in] characteristic to lower the nose in a stall is reduced. More seriously, too far aft C of G will dramatically effect spin recovery. During spin testing of a Cessna Grand Caravan I flew, I was required to demonstrate the spin recovery at both C of G limits. The forward limit test was straight forward. Very nose down, and a high rate of descent, with high speed and G recovery, but predictable and recoverable (I put a video clip on Youtube a while back, "C 208 spin" or something like that). The same aircraft at the aft C of G limit would not lower the nose well when I moved the controls forward. I held the control wheel hard forward against the stop, as the aircraft spun around nearly level, though going down flat and vertically. The aircraft did recover, but very differently than the forward C of G. I sensed that there was not much more control available to me to recover the stall.
So what I learned was that in "normal" flying, you will have less sense of how the plane is loaded, or misloaded, but, during more extreme maneuvering, you may find shockingly that the plane will not do what you expect it too.