What Exercises Are Good For Weak Lower Back Muscles?

Start out with crunches, with feet supported up on a chair, bed, or something high.  With hands behind the head supporting the neck, lift slightly, just enough to raise up the shoulders, then back down again.
When you get stronger, then pull your knees towards your head as you lift.  After that, side-to-side, lying on the floor, bend your knees and take your fingertips and going side-to-side, touch the outside of your foot in a quick motion.  Good luck......been there, am there forever after two back surgeries.

A big ball is an excellent way to do many exercises with support.  This will help you strengthen your back without over exertion. I recommend visiting a few gym franchises and speaking with some personal trainers to get some insight on various exercises that will help you workout your back safely.