You just parented the leg to the leg controller, it is not the correct way to do it, so first thing remove this parentage:
Instead join all the objects together with CtrlJ, then select the object, shift select the armature and CtrlP > Set Parent To > (Armature Deform) With Empty Groups. This will create as many vertex group in your object as you have bones. Now select a limb in Edit mode and assign it to the correct vertex group (there's a problem with your topology though, as it is not aligned with the bones, so you maybe fix that before assigning):
Another solution would be to parent With Automatic Weights and let Blender assign the vertices itself, if it gives good results.
Also maybe the bone called Back_body should be reversed so that it points backwards.