Charter 757s have been going from Europe to the Dominican Republic for some 20 years now, in fact from European points like Munich which are a lot further away than Dublin. They too stop at Bangor/Gander etc to refuel.
The 737 and the 757 fuselages are identical cross-section. If you are not an aircraft buff you would never notice a dimensional difference.
Stopping on the way also allows the aircraft to be serviced, cabin cleaned, lavs pumped out, rubbish dumped, etc.