@jimschmidt wrote:
....if I choose yes it says spline curve vertices have been added).....
When I tried convertpoly I get the choice heavy or light but either choice gives me "0 objects converted)
....
That shape is made of Polylines that have had PEDIT's Spline option used on them. You can tell by the control points not being on the curve, and there not being any mid-segment grips:

That's one of the situations where "heavy" 2D Polylines occur -- they result from applying that option or the Fit option to a "lightweight" one. Those can't be CONVERTPOLY'd [as you have found], and it appears WEED doesn't want to work with them, either. You could try PEDIT's Decurve option on it first, and then try WEED again.
I haven't loaded WEED to try [because I virtually never have "heavy" 2D Polylines], but PLD was written pretty much to do the same kind of thing to the "lightweight" ones. I forget WEED's particulars after all these years, but if PLD's operation is similar to it, that distance option is a maximum distance to straighten. It won't remove a vertex if it will result in a segment longer than that maximum. Even in the LWPolyline [the cyan one] in your drawing, which you can apply PLD to, if that were a "heavy" one that you could apply WEED to, your 0.1 distance choice is much too small for any vertices to be removed, because the spacing between vertices is mostly in the 1.0 to 1.5 range. You need to give it a distance that is greater than the length of segments you want reduced in quantity.
But of course, the reason for the high number of vertices, and for using PEDIT's Spline option, is to achieve a reasonably curvy appearance, or actual smooth curvature. If you remove vertices, it will get "kinkier," so you need to decide how kinky is acceptable.
[I need to revisit PLDiet, under newer versions than it was written in -- it's not behaving right on the cyan Polyline in your sample drawing. I couldn't say whether WEED is similarly affected by version.]
[[EDIT: No, maybe I don't -- I find that your cyan LWPolyline has large numbers of coincident vertices, which can cause problems with all manner of things. The second vertex location has 8 vertices, all in the same place! The third location has 9, and the fourth location has 12 ! When I got rid of those with OVERKILL, PLD worked as expected. I couldn't say whether WEED would have trouble with similar conditions.]]
Kent Cooper, AIA