Is there anyway to use weight paint to determine the influence on different parts of an object while using the cast modifier? If not, is there any other way something like this could be achieved (maybe something with vertex groups)?
This is what the Vertex Group option is for:
- Start weight painting; a vertex group will be automatically generated.
- Select that group in the cast modifier:
Note that Vertex Groups and Vertex Weights are really the same thing; the weights seen in Weight Paint mode belong to the highlighted vertex group in Properties > Object > Data > Vertex Groups.