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After receiving a good answer to my question I'm trying to learn how to deform my "egg" changing the radius of the control points.
It works, but I don't understand how to avoid the "angular points" on the surface:
As you can see, in both bottom and top center the surface is not smooth anymore. Is there any parameters I have to set before scaling the radius of the control points or have I to apply a modifier after?
This is just an unfortunate consequence of the conversion to mesh in the Bevel. With linear interpolation, 'Round', centred on the curve, causes self-intersection on the inside of the sweep, as on the left:
The middle example shows the curve with its U and Bevel resolutions reduced, and its 'Radius' interpolation set to 'B Spline'. The last example is further tweaked to try to capture the spirit of your original. Its resolutions have been further reduced, and a Subdivision Surface modifier assigned at level 1. This aims for a nice even tension of the mesh across the surface, with squarish faces of a roughly even size.
If you wanted finer control. you might use a curve-circle 'Object' bevel, instead of 'Round'. In that case, you could offset the object-profile with respect to the path (by shifting the profile in Edit Mode), reducing self-intersection on the inside of the bend.
Under Active Spline choose Interpolation Radius > Bspline, it will smooth the shape:
Also you'll need to move up the handles a bit:
