The bands provide constant tension on the muscles and are much more efficient, whereas weights create less resistance when arms or legs are bent at at more acute angles - like in bicep curls there is less resistance the further you curl up, same with tricep extensions, leg presses, etc. Weights are still wonderful and work great for strength gains and will still fatigue your muscles, but the bands work your muscles in a way that weights cannot by working every bit of your full range of motion.
Missy