Have you got a diagnosed back problem or is it just weak?
If it's just a case of a weak back then you should do some back strengthening exercises first, which will help you to avoid back problems in the future.
Have you got one of those 'Fit Balls'? If not, try and get one, I think Argos and some large supermarkets sell them.
For the first week use it as much as you can to sit on...at the pc, watching tv etc. That should wake up your back and abdominal muscles.
For the second week start with back strengthening by laying on the fit ball so your tummy is on the fit ball and your feet are on the floor but steadying you against a wall or a chair. Gently clasp your hands behind your back and then lift your back up as far as is comfortable, hold a second and then down.
You don't need to do too many of these lifts initially...maybe 10 or so, so long as you do them daily.
The third week you should notice your back becoming a little stronger so you can increase the amount of lifts as you feel you can do.
Also in the third week you can start on your abdominals. Again, with your feet on the floor but steadied against a wall or chair lay so your lumbar or lower back is on the fit ball. Cross your arms over your chest and then lift up as far as is comfortable.
Again, you could start with 10 but by day 4 you should be able to do 2 sets of 10 with a couple of minutes rest between sets.
Over the following weeks increase the amount of back lifts and abdominal exercises as you feel stronger. The important thing is regularity...do some every day.
It won't be long before you can feel and
see the difference.
However... if you can't do any of the above due to a back injury then you should probably get some GP advice and physio to try and correct it because I'm sure you know, that as you get older a weak back is likely to get worse.
Hope this helps... feel free to message me if you need to
