No, it is not currently possible to key weights in Spine. Weights define how bones influence vertices, and these relationships remain constant throughout an animation.
However, there are alternative approaches that might help achieve what you're looking for:
Using Transform Constraints
Instead of switching weights between bones, you could use transform constraints to control which bone has influence. By keying the constraint mix values in your animation, you can smoothly transition control from one bone to another without changing the actual weights.
Swapping Attachments
You could create duplicate meshes with different weight configurations and swap between them during animation using visibility keys or by switching attachments in a slot.
Multiple Bone Setup
You can weight a mesh to multiple bones simultaneously. By animating those bones differently at different points in your animation, you can achieve varied deformation without changing the weights themselves.
While keying weights directly would provide more flexibility, these workarounds can help you achieve similar results for most use cases. The weights system is designed to remain static to keep animation data efficient and manageable.