There are many weight exercises that have benefits to you and your physical fitness. There are some weighted exercises that can cause severe problems if not properly executed. Although I am not someone to avoid an exercise because it can be executed wrong, I believe there are better alternatives than those exercises. Isolation-type of exercises can cause problems and do not serve a functional purpose. Doing leg extensions and leg curls seem like great exercises for the legs, but you can do better with back squats or dead lifts. Compound movements such as lunges with bicep curls are much better than these isolated exercise movements. But, I would avoid these two back exercises because you can cause serious injury to your back. There are much better alternatives.
The first exercise I would avoid is the weighted good morning exercise. This is done by placing a barbell on your back (like you are going to do a squat). Then, with both of your legs straight, you bend over forward and go back to the starting position. Maybe, it is a better exercise with no weights on your back but this exercise can cause serious back injuries. The late Bruce Lee injured his back while doing some of these weighted good morning exercises. I always wondered why it is called a good morning exercise. You have to make sure that you keep your core tight or you will get injured. Back rows and dead lifts are a much better alternative. If you need to work on the lower back more, try hyperextensions (reverse crunch) either on the floor or using one of those hyperextension benches (apparatus). But, you will get great back development by doing the dead lift and back rows.
Another exercise that I would avoid is weighted side bends. This is done by holding dumb bells overhead and then bending to the sides. Personally, I sprained my back very bad doing this exercise. I made a huge mistake of not tightening my core enough when doing this lift. It does impact your stabilizer muscles in your core, but if you make a mistake, you will get hurt badly. Try doing one-armed barbell presses. They hit the stabilizer muscles of your core. Make sure you keep your core tight. This is not the time to relax them when doing these exercises.
Using weights on the good morning exercise and side bends are dangerous if not executed properly. The key is to keep your core tight and not relaxed. But, as I mentioned, there are better alternatives in the dead lift, back rows, and one-armed barbell press. Always keep safety in mind to prevent injuries.