Hey Vurt,
first thing you need to do before you bind the skin is create the necessary blendshapes you need.
Do a test animation from A to B, with no arm movement, using your keyframes. For example. Your baby would start at keyframe 1 and end at keyframe 48 lets say.
At frame one, this is how your baby will look fully deflated.
Go to frame 48 (or the frame the baby stops deflating). And duplicate it. Move the duplicate next to the original, and edit it (shrink it), to how you choose.
Now, select the duplicate, shift select the original and
Deform > Create Blendshapes ...tick the box and enter an appropriate name, then click create.
Now hide or delete the dup copy.
Go to frame 1. Select the baby. Go to Window > Animation Editors > Blendshape.
Press select then key.
Go to frame 48. Move the slider up, then press select then Key.
NOW you are ready to bind, then add movement to the limbs
good luck
those who succeed are only the failures that never gave up.
https://www.vimeo.com/7080130