try drawing manual edges horizontally between your vertices. It looks like the internal edges are not optimal for the deformation you're looking for.
Here's an example:
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On the left, without manual internal edges
On the right with manual internal edges
After weighting bones and rotating the bones the deformation for each look like this:
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To draw the internal edges just click and drag from one vertex to another in Edit Mesh
mode.
See Meshes - Spine User Guide: Edges for more.