Curve To Mesh + Spin tool

I’m trying to model a wine glass.
I modeled the cross section using curves, converted it to a mesh, and used the spin tool to make a nice glass.
BUT, the glass has no thickness… It is clearly visible mainly at the rim of the glass.
How can I make it a little thick? I tried to duplicate the curve, shift it slightly toward the spin axis, and rotate it. This worked, but it maked the glass a bit awkward.

Any advice?

Your Cross section should look like this before spinning.