What can I do, for I cannot read documents on screen for long times, but my required readings are too heavy? 1) My degree demands me to have around 50 lbs. of new books and reading each year. Second-hand books are not possible for my subject that changes every year.

2) The total cost of all this material is around $5000 USD. 

3) I must have all this material with me while I travel repeatedly between North America and England during my degree, and I cannot afford exorbitant shipping or airline baggage fees each time. 

I suffer from an eye condition that forbids reading on screen for long times. Thus buying the PDF versions for these books is not a possibility. What else can I do?
e-ink

As also suggested in comments, a quality e-ink reader as (for example) the better Kindle models will provide a paper-like experience for your eyes at a limited weight.

PDFs are not the optimal form for that (ebook formats allow re-flowing to have screen-sized full pages at a font size tha't best for your eyes), but it will certainly work; reading hundreds of pages on that is more like reading a book than a screen.