Even if you're young you can get a weak back. Especially if you sit in an office all day. I know. For bike riding, your back muscles need to be strong enough and have enough stamina to keep your spine locked up for a long time. I suggest core exercises:- (i) hyperextensions (but don't extend past straight), (ii) sit ups, (iii) side raises on one elbow. Those will give you strength but not necessarily stamina. For stamina you can ride more often and build up the distance. A rowing machine might help too.