I once left about 30 paperweights on a plastic table in my conservatory for an hour or so, in bright sunshine. The antique weights or flatter modern weights caused no problem. However, a couple of Mayauel Ward weights caused significant black burn marks. I only noticed after I picked one up, and burned the palm of my hand whilst looking at it! The shape of the weight (near spherical) combined with the design (mainly clear glass) was the cause of the problem.
I try to keep all paperweights out of direct sunlight: if you leave older Ysarts or Bohemians in sunlight, expect them to go purple more rapidly (due to precipitation of the manganese which was added to the batch to counteract the natural green colour from iron in the sand).