Is the increased weight of the ipad 4 worth the retina screen, in comparison to the ipad mini?
No. Unless you are showing clients pictures or using a remote desktop access to control a computer and do work, the mini is so much lighter than the retina iPad that it's not even fair to compare them in terms of ease of use.

Yes, you can tell the difference between something drawn with retina versus the mini screen - especially for foreign texts and line art, but in practice it doesn't matter much.

I have and use both and easily, my use slants 10 to 1 in favor of the lighter mini - especially for short bursts and casual reading and gaming. For several apps, I do increase the font size one notch from what I prefer on the retina display, but I don't find any critical failure in not having a retina display despite using the device heavily for work and pleasure.

At half the weight and almost all the power, the mini is the device to get except for some very specialized situations. You can also put the money you save into AppleCare plus or a wireless keyboard or just apps and have a better all around solution.