This is why cross training is so important, especially for those of us with desk jobs. The problem is not actually weak back, but a weak abdominal core.
Pilates, yoga (power type yoga, not hatha), strength training, etc.. are all going to help your core and your riding. I have a bad back from riding and what keeps the pain at bay is being at the gym a few times a week, going to hot yoga twice a week and doing at least a little strength/core training every day.
They say money doesn't buy happiness -- well happiness doesn't buy horses!