My pen weighs in at 10g in my backpack and is capable of durably recording information for thousands of years. No battery to charge, cheap, and plentiful.

Only if you're writing on parchment, paper only lasts a few hundred years.

I use my fingers to interact with computers, and they don't have any extra weight at all, as they are already attached to me. You need to also count the weight of the paper.

And, no, your pen and paper are not able to durably record information for thousands of years. Unless you have some really bespoke setup.