Actually, it is a lamp base - cheapo job from Homebase.
The weight in the base seems to be a plaster casting painted black. with a hole in the middle for a nut and washer to hold it to the central stem. On one, the plaster has broken away around the nut and washer.
I strated out thinking "unscrew nut, recast centre of weight, refix" but after 5 minutes trying to move the nut on the hollow shaft I thought "why not just glue the base to the weight".
So - what to use? Had a quick go with PVA because it was there next to me, but I don't have full confidence. We shall see.
If it fails, how about "sticks like sh*t" or "no more nails" or similar?
Cheers
Dave R