Will body weight training help with my overall mobility/flexibility?
If you do them properly, yes.
When using your body weight, it will be much easier to go full ROM. It is a good way to train your muscles to get used to extending to, and working at, full length.
When trying an exercise for the first time, it can be a good idea to try in with just your body weight first. This way you can get into good habits once you move onto lifting weights.
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