Nice experiment!

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.

You are right. This is just an exploration. The main motivation was to play with the pressure input from Apple Taptic engine. I was trying to applying "physical" properties to virtual objects.

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

I don't think the visual approach does much for interactions, so that's a separate concern. This is more about feel. E.g. inertia applied to CoG, so when you grab it outside CoG, large files will tilt more as you drag. Light files would probably start spinning even.

Now, applying inertia for the movement itself would be annoying. Please don't do that. :)

I’ve often wanted a setup where it became physically harder to send an email to me the more unread ones I have to deal with. Like having to cram an extra letter into a pigeon hole that’s already full.