Dont use Subdivision modifier, rather go to *Curve > Set Spline Type >* **Nurbs**

Also move vertices to origin center to let snitching follow the curve.

[![enter image description here][1]][1]

[![enter image description here][2]][2]

Origins of all participated object has to be on the same place.

[![enter image description here][3]][3]


  [1]: https://i.sstatic.net/lsVwD.png
  [2]: https://i.sstatic.net/Tkt3v.png
  [3]: https://i.sstatic.net/zQgSi.png