There are two ways to get the bones to influence your sprites; by parenting them or by skinning them.
You could manually parent your sprites to the bones, but to speed this job up Puppet2D has a button that does all of your object in one go. Select all the bones and all the sprites/objects and click “Parent Object to bones”. This will parent all your objects to the nearest bones.
Skinning allows single objects to be influenced by more than one bone. In order to do this the sprites need to be converted to a mesh. To do this select your sprite (make sure its not parented) and click “Convert Sprite To Mesh”. You can change the number of vertices in the mesh by first adding a polygon2Dcollider component to the sprite. You can use this to remove and add vertices before converting it to a mesh.
To bind the mesh to the bones, select all the bones and the skin, and click “Bind Smooth Skin”.. Your mesh should now have a Skinned Mesh Renderer component on it. ~If you move the bones the mesh should move with it.
To start editing the skin weights, select the mesh you want to edit and click the “Edit Skin Weights” button. You will see a bunch of vertex objects parented to the mesh. If you select the vertex you will see a list of the bones that influence the vertex followed by their weights. To edit the weight values or influence, just change the values in the inspector. If you want to change multiple vertices at once, change the value and click the “Update Skin Weights” button in the inspector.
To finish Editing weights click the Finish Edit Skin Weights” button, and the vertices will be removed.