It is very odd. I had not noticed anything when I took the photo, and this photo is one of several I took of the bird at the time yet several of them show no sign of an overgrown bill. I shall have to have a close look at the bird, but even if the overgrowth existed it could have become detached by now as it would be very flimsy - I had an elderly Spreo Starling like that; it developed a little bit of an overgrown bill that I was going to clip, but it beat me to it on the first occasion the overgrowth occurred.
Confusion now reigns. I spent several minutes at the end of the day watching both cock Napoleon Weavers and at first I could not see anything unusual. After a few minutes, however, the apparent appendage had appeared on one of the birds. I bent down for a closer look (the bird was in a shrub) and there it was, but the weaver seemed to be moving its beak as though it was eating whatever it is - it may have been an optical illusion, but "the thing" appeared to turn upside down. A few seconds later it had disappeared altogether and there was nothing protruding from the bird's beak. It is still very odd!
Yesterday I watched a Napoleon Weaver cock on the floor of the aviary pick up in its beak something that looked just like whatever it is in this photograph. The bird then proceeded to eat it.
Interesting. If you look very carefully at the photo it does appear that the 'curved item' is being held in the bird's beak, and is not actually part of it.
