As someone with large breasts, ans someone who knows a lot of women who have large breasts, it all depends on your bra. Having a well fitted bra is a MUST if you want to avoid back pain/future back problems. Make sure you go to a store where you can get measured professionally. If you think you can, you can always measure yourself with a tape measure, and an
online guide.
Having good posture is also important. If you slouch a lot, you'll just give yourself problems. Make sure you sit/stand up straight with your shoulders back, and your head up. It should help.