In reality, all guitars sound different, and each instrument brings its unique sonic signature to the table. Many factors can change a guitar's timbre, from the pickups, the materials used and, of course, the weight.
Many players report that lighter guitars can be more resonant and vibrant, with a tone that sounds a little more alive - with some guitarists just preferring the way a more delicate guitar reacts to their playing.
One player who will always pick a lighter axe is slide master extraordinaire Derek Trucks, saying to Premier Guitar, "I found most of the time, if you go through five or six guitars, the lightest one is probably gonna sound better. I don't know if it's older wood or dryer, but they seem to speak a little bit better".
That said, not all players feel the same. Some guitarists swear blind that a ponderous Les Paul will have more sustain and there for a much better tone. Really, it all comes down to personal taste and the particular guitar you're playing. So try some guitars out and find the model that speaks to you.