The line which defines the Ellipse entity in AutoCAD is a Spline. It is not possible to edit the width of a line created as a Spline. (At least we do not know of a way.)
Recreate your Ellipse as a pline. Type the system varaible, PELLIPSE at the command line and set it to the value of 1. Now redraw your Ellipse. It will be a Pline. Use the PEDIT command to change the width.
More discussion about this topic on Augi:
Convert Ellipse to Polyline
