Thanks for the reply. I would have acknowledged sooner, but I have been having trouble getting onto the web site. I also did a Google search, but the only link was a web site that does not seem to be active, so I could only see as much as appeared in the Google window. I checked with the person who was trying to remember the song, who pieced together a third verse:

The WheezWomp is nice, but it's lazy.
It won't build a nest of its own.
It hides from the rain neath a daisy,
And cries when you leave it alone.

This person's recollection was that in the second verse: "Its wings are too curly to fly with", which sort of fits better than heavy wings with it floating on the breeze.

Still hoping to find a lead on who recorded the song, but thanks again for your reply.