Now, applying inertia for the movement itself would be annoying. Please don't do that. :)
When you mention CoG, spinning etc. it becomes game-like — not something I would want in a productivity focused interface. But if you're developing a game or a toy experiment, go for it.
Designing for visual is what is missing, I would want to work on the visual plus audio to compliment the "heaviness" I think someone else also mentioned in the comments on experiments with audio to express physicality to
Maybe an IDE that semantically tints code sections?
Subtle red tint for code that is highly coupled, historically prone to breaking, or has high severity if it fails. A yellow tint for business logic or code scoped to a singular user or action. No tint for pure functions, UI components, and utility code.
I agree that providing something more tangible than just a number would be beneficial for some operations. But I think it would get annoying quickly. Having difficulty moving a "heavy" file is the opposite of a good user interface. Every manipulation should require as little mental and physical effort as possible. Apart from that, I can't apply force with my mouse — it just clicks.
I believe a purely visual approach could work well. For example: every file icon has the same front area (basically the rectangles we have now), but visually extends to the back with some sort of stylized 3D effect, according to file size. So a small text file looks like a thin sheet of paper, a 10MB file might look like it's made of thick cardboard, a 2GB video looks like a box with considerable depth. The scaling should probably be logarithmic, not linear, to work well with human perception.