Check out 17 minutes into this video, learning about show mesh and changing to contour:
2 things I noticed:
1. The left arm is very close to the body and the right arm is overlapping it - if those aren't independent, they risk pulling the resh of the mesh with them. In your case I would add a + in front of your left and right arm groups, and then staple them (also in the above video). Then when you drag them, they won't pull the rest of the body.
2. The heart is being considered part of the mesh too, and will definitely mess up how warping works. In general we recommend having all the character parts connected into one continuous mesh - if you don't want that to move, consider making it a background element instead. If you do want it to move, consider making it independent (add a +) so it can act on its own.