If the sides are almost vertical, then it could be a cut down from a domed and flute-faceted weight. If the sides slope out towards the top then it could fit better with a regular sized faceted weight. But Roy is certainly the man to confirm or deny my thoughts as I only have one example each of those type of Whitefriars weights, and he has a house-full!
If I am right, then in either case, the way the top is repaired with an inward slope from the side would fit with a repair that has removed the lower parts of original faceteing, which would have had a reasonably noticeable inset into the dome. The shallow (new) dome of the top (if I have understood this correctly) would fit with a repair retaining the shape of the cane setup which would define the dome. If it had been finsihed flat or concave, it may have cut down too close to the canes.