Dynamic physics on procedural mesh

I built a Mesh generation Script that I assign to an empty Game Object, which then creates from scratch triangles on a Mesh Filter component and renders using Mesh Renderer.

Everything works great, one thing I am trying to resolve is to how to then convert this mesh to respond to physics.

An example I can think of is Unity's Tree where branches respond to wind. Is there a way to get similar effect without moving the vertices manually? (My mesh extrudes around a spline so maybe I can bend the spline to get the same effect?)

But another effect is to hang a heavy object on this branch and have it bend towards the ground.

I can't think to inifinitely many scenarios, so maybe I should build around these two cases, but if there is a more general solution I would like to know about it.

Thanks!