Any correlation of sound quality to weight has to be predicated by amplifier topology. Traditional tube amplifiers probably have the strongest correlation here, because the size of its transformers (power plus 2 outputs) generally dictates how much power can be provided at reasonable distortion levels. ~ 1 pound per stereo watt is not uncommon. Of course the raw power itself isn't a perfect correlation to sound quality, but the weight (transformers) is definitely a big factor in distortion and bandwidth. This is how people got an inking the Carver amps weren't on the up-and-up about their power ratings (only 19 lbs for 75 stereo Watts is a red flag).
Next is high-bias class AB and class A solid state amplifiers, which require large amounts of heat sinking and still a very large PSU (power transformer). I'm a tube guy but I'm still quite fond of some of these.
Then you have class D which can be made extremely light relative to their power output, and the correlation becomes very weak. They can sound good! I don't hate them; they're just not my thing.