I suffer from an eye condition that forbids reading on screen for long times.
The weight and the travel are not the primary problem here. The eye condition is the primary problem, and this way of looking at the situation will give you the key to finding a way to work more comfortably.
In the U.S. the people to talk to are the Student Disability Office at your university. I don't know what the analogous office in the UK is called.
You will be asked to document your eye condition.
Once you're set up with a Section 504 accommodation plan, your university will find solutions. Obvious first choice, audio recordings, if they already exist. To some extent, it would be good to be able to work with digitized PDFs of these readings, which you will keep on a special laptop whose display has been optimized for your particular eye condition.
It used to be, a human reader would record texts for the low vision student. Now, they will set you up with software that reads the text out loud to you.
You need not be legally blind to be in need of accommodations. They will take into account that you can do some reading, but tire more easily than the average student, and need support.
I suppose it's possible the publishers will lend you a second hard copy so that you have one copy in each country. You just have to talk things over with the disability office. You will work together as a team.