It could mean your hair is weak, if you're sure it's breaking and not shedding. (Shedding results in long strands with a bulb at the end.) But I think your hair could also break if you don't handle it gently during the braiding.
Is your hair relaxed or natural? I think a lot of people deep condition their hair before putting in braids or getting it relaxed. This way it's ready to stand up to the "manipulation" during braiding (and support the extensions, if you're adding some) and to stand up to the chemicals during relaxing.