so I'm trying 2d animation and Iam facing a problem now. Which is that when I'm in pose mode and I move the bones of the hand, the mesh of the hand moves, but when I move the bones to high, the mesh doesn't follow up and has like a gap.
If you use Vertex Group in Armature Modifier, be sure Weight Paint of the object is absolutely red.
Or leave Vertex Group field empty.
Be sure other bones (small one) doesn't have influence to the object. Select Armature + Object, switch to Weight Paint mode and click on other bones to see if object is completely blue.
In your case Delete Armature Modifier called "Armature".
As you can see the other bones have influence on your mesh as well:
So either substract all influence in Weight Paint mode or go in the Vertex Groups list, select the groups that are not supposed to influence this bone (Bone and Bone.001) and click on the Remove button (or in your case you can even delete them):
Maybe next time for this kind of object, instead of parenting With Automatic Weight, use With Empty Groups then assign manually, or directly parent to the bone if the bone is supposed to control the whole object.
Not sure about your rigging though, why several armatures for example? You may have your reasons...