Something I find very interesting in character movement is to make them feel weighty despite models having no physics behind them. How would you accomplish this feeling?

You should really read my Animation Primer. The first post answers your question:

[Animation Primer (Part 1): Core Principles] - The 12 principles of animation and how we add the feeling of weight and speed to things that inherently have none.

[Animation Primer (Part 2): The Third Dimension] - The major benefits of moving from 2D to 3D and some basics on how we do it.

[Animation Primer (Part 3): It’s Automagic!] - Some ways we’ve figured out how to use technology and simulation to augment and improve our ability to animate movement.

Got a burning question you want answered?