Any information about difference between the two types will be helpful!
I assume that you're talking about the action of the keys. If so, I covered this in a recent answer about MIDI controllers:
The key action is a matter of how hard it is to push the key down before you trigger a note. A real piano key has a bit weight to it and requires more force to push it down than a synth. This is a good thing for dynamics because it makes it easier to play the softer notes which in turn means that it's easier to play a wider dynamic range of volumes.
MIDI controllers that attempt to mimic that piano feel will be marketed as "hammer action", "fully weighted", or something similar. Those with no weight at all might call it "synth action" or avoid mentioning it altogether. In the middle is "semi-weighted".
Again this comes down to if you want to play like a piano player. If you are playing anything non-synth (piano, electric piano, etc) then being able to play dynamically is pretty important and I'd look for something with hammer or at the very least semi-weighted action. Other than that, it's up to taste. Try some out at a music store if you can to see what key feel you like.
So essentially, when a key action has more "weight" it's harder to push down. That might sound bad. But it actually means that it gives you more control over the volume.
"Lightweight" and "heavyweight" are not actually differentiating the force you need to apply in order to get a differentiation in loudness, but rather the momentum. A weighted keyboard has inertia on its keys (generated by some lever+weight mechanism that might actually warrant decoupling a digital piano from the floor). This is different from a "semiweighted keyboard" which is not much more than harder springs, but no inertia.
As a result, for a weighted keyboard the accelerating action taken before the key strike is more relevant than with a merely resistive keyboard where more of a distinction is made at the time of striking. Graded loudness and fine-grained articulation is easier to do with weighted keyboards. The release, in contrast, is mushier. For basically percussive sounds (piano, harpsichord, clavichord, celesta), weighted keyboards are the best choice. For continuous-sound instruments where the release is as important as the attack (organ, harmonium, accordion), a weighted keyboard is a distraction.