I'm no expert, but I used to have back problems. I'd say they were due to both 1.tension held in the back and 2.weak muscles. Usually my back was ok, but from time to time I'd lift something, or twist funny, and put my back out for up to a week or more. I'd be in a lot of pain and discomfort. About 11 years ago I saw a chiropractitor who recommended I try Pilates. I didn't go to a class but found a Pilates video instead. I followed the very simple instructions to the introductory exercises (about 20 minutes) each day for several months, and my back improved tremendously. Pilates is very core-strength building and relaxing. Since then I've had few problems. Even if I accidentally twist my back and end up in pain (this happens about once a year), it's not too painful and it heals in a couple of days. It's only my knees, ankles and buttocks that complain if I meditate for too long! (But I don't sit for longer than 1.5-2hrs anyway). I don't do Pilates anymore because I'm now more into
qigong (also excellent for core-strength and relaxation).
So find a regular exercise to both 1. relax and 2. strengthen the back. (I don't think just core strength on it's own is enough, though I'm no expert!). Personally I'd highly recommend qigong, but with a good teacher, as they can point out poor posture and where you're tense (see above link).
It might also be a good idea to have an expert check over your back.