Weak abdominals are not always to blame for low back pain. Usually tight hamstrings are the culprit. Fitness testing may help determine the origin of your pain. If you score high in the bent knee curl up test, but low on the sit and reach trunk flexion test, focus on improving your hamstring flexibility. Muscles can be short or overtight from disuse.
Poor fitness leads to poor posture.
If you carry most of your weight in your abdomen, your back muscles must counterbalance. The same is true concerning the relationship between your quadriceps and hamstrings. Tight hip flexors and hamstrings, combined with weak abdominals and upper back may be a prime cause for your suffering. Drop your pen on the floor. Bend down to pick it up.