If it's feeling very weightless, there's a good chance that you're letting the computer do too many of your "in-betweens," and you probably need some breakdown poses in there to properly describe the body mechanics. My advice would be to act out and/or film the action you are trying to animate, and really study all the small actions that happen in between the larger actions (small things, like when you shift your weight a little bit, what happens to your shoulders, feet, etc?) – that's the stuff that will make things feel correct. Another culprit might be timing – if your timing is too fast, there is a chance the characters will feel very light, however if it's too slow, then the characters will feel floaty! The trick, then, is to study the actions you want to create, and then exaggerate the poses and timing to fit the style you are looking for, while placing the fast bits and the slow bits in all the right spots to create the feeling you are looking for! It all starts with studying reality whenever you can, and then applying your artistic eye to that reality in order to create something special.
And the most important "weight" tip for any creature is always to simply make sure that no foot is ever off the ground (except during a run sometimes) unless the hips are over the opposite foot.
- Shawn :)