I am trying to make a cup with varying thickness. The top of the cup is much thinner than that of the bottom part of the cup. I have tried playing around with the Clamp but it doesn't get the bottom to raise up as high as I would like. How do I get an affect like this?
You can for instance use a solidify modifier set to vertex group, then paint the weights in weight paint mode.
First add a vertex group and in edit mode make sure to remove every weight from your vertices.
Then add a solidify modifier to your mesh, set the factor to something > 0 so there is at least a bit of displacement with a weight 0.
Then go into vertex weight paint, with the ALT key pressed left-click on the bottom of your object, then drag your cursor up to the top and release the mouse button. You will see a gradient on your mesh :
Play with the solidify and the vertex group factor. Tweak a bit the mesh and use a negative thickness to get something approaching your image. Final result :