At night I lay awake looking at the darkness, listening to the silence, prefiguring the future, picking out of the past the scraps I had overlooked, those rejected events which now came to the foreground, large and important, so that the weight of destiny no longer bore on the current problems of my life, whatever they were at the time (for who lives without problems every day? Why waste the nights on them?).
I looked up the meaning of "bear on" in the dictionary but then again I want be sure about my understanding.
bear on something means: to relate to or possibly influence something
so can we say the sentence in bold means: she no longer believed in destiny and she thought her problems didn't caused by destiny?
source: A Far Cry From kensington by Muriel Spark