How do the lighter Amps compare to the heavy weight Amps is terms of quality of sound, heat build up during long operations, and overall longevity? I thought the heavier ones would be better. Is that the case with the Amps?
Weight can be an indicator of quality, but you have to know what you're looking at. I'm also going to assume this discussion regards Class AB amplifiers, because switching amplifiers or those with innovative power supplies can weigh a lot less and not suffer any in quality.
As lsiberian brought up, for Class AB amps the transformer is typically the heaviest component, especially if there's more than one of them, but there can be other components that contribute significantly to weight. For example, heat sinks. Most amps are passively cooled, so they often have heavy heat sinks to absorb and dissipate heat. On lightweight amps it might be cooling that was skimped on. On some amps the chassis and case can be very heavy, and for little practical reason. Sony used to be famous for this, getting even some of their CD players to weigh over 30lbs. Many very expensive amps have needlessly fancy cases and facias that add a lot of weight, but no practical value. Other components of the power supply can also be pretty heavy, like if the amp uses solid buss bars for power distribution, or large arrays of smoothing capacitors.
So, if an amp has a modest chassis and case, yet it weighs more than other amps of similar power ratings, there is a reasonable chance that the manufacturer of the heavier amp gave it a more robust design. It may be a higher rated power transformer, it may be a more capable power supply, or it just may be more heat sink mass to keep the amp cooler under high load conditions, but there's a reasonable chance it's something good.
That's not to say that weight should be a primary indicator of amplifier quality, especially sound quality, just that in some cases it can mean something.
Another factor to consider, unless you have *very* good speakers that can play very loudly without distortion, and you have a large room to let them breathe (and use a lot of power), you are unlikely to hear differences between any two properly functioning solid state Class AB amplifiers.