Character is being dismembered

I was looking a bit more closely at your rigging hierarchy. It looks like all the artwork layers are independent with no artwork at the root. That will not work. What you need is artwork for the torso that is NOT marked as independent. That would go under the Body layer. E.g. the chest and shoulders. (I normally include the legs as well - I normally don't make them independent.) The arms and head layers are then marked as independent., but the artwork has to overlap with the body so it can attach to it.

Think of cutting out bits of paper (arms, head, body, etc), then putting a pin through the head piece of paper through the body piece of paper behind it. If there is nothing behind for the pin to go through, the two pieces of paper will not be connected. So I often draw a tall neck as a part of the torso layer, then the head attaches the to extended neck. (Either that, or I don't make the Head independent.)

The arms at the should is the same. You need the torso behind the shoulders of the arms piece of paper. Your arm has to overlap and attach to the torso layer behind it. So at all times if something is independent, you need to think about what it is going to attach to. And that artwork has to be included in the bit of paper for the parent (ie not independent).

(Oh, and the formal term for "bits of paper" is "mesh". It is important to understand when to and not to use independence. You cannot mark everything as independent as it will all fall apart. You need to start with something (e.g. the torso) and attach additional body layers to the parent layer.

The eyes and mouth etc can easily be independent as they are in front of the face layer

Could be a bit of both. Some suggestions (but won't be enough).

First, it is normal to put a root level "+CharacterName" at the very root. You have Body and Face both at the top level. More normal would be:

+BigGuy

    Head

        Face

    Body

        Arms

        Legs

You have Head under Body for example. That might not work out so well (not sure - but its different to what is normally done).

When you have independent layers, the child needs to overlap the parent layer artwork so it has something to join to. This can just be a blob of color behind the arm for it to attach to, but the origin marker should be green to show attachment. You LA origin is yellow. That means it is not attached to a parent (the body).

There may also be tagging issues - for example, the Left Shoulder tag must be on the body layer, not the arm.  It would be good to see the Body layer highlighted as well, to see if all the Waist etc tags are in place. CH has to understand the skeleton to move the puppet correctly. From the handle count, I am guessing you might need more tags on the body.

Feel free to ask more questions