The time frame for the Paul Ysart badge weights is thought to be 1930s. These were made as personal requests and were no doubt in the category of "beer money" weights.
It is quite normal for a side cut to be made in order to allow the weight to be viewed in its "upright" position. I think that side cut examples are fewer than uncut ones.
As for the "pitting" question, I raised that with Dave Moir as I had a theory that perhaps the pitting seen on many Vasart weights could date them as early period. My thinking was that the pitting was caused by the not-too-efficient "moving tray" method of annealing used in the early days at the Shore Works. But my understaning now is that such pitting can occur whenever or wherever an item is in contact with "bits" of some form while it is still hot. Even some Paul Ysart weights show a degree of pitting (and I should have noted that before I raised my question with Dave).
Incidentally, there are opinions in the paperweight world that at least some badge weights like those attributed to Paul Ysart may well have been made in Belgium!