For Paul Ysart examples of "Medallion / Cap Badge" weights, the dating is stated in Colin Mahoney's book, Masterworks, the paperweights of Paul Ysart as: "During the 1930s and possibly during World War II ..."
Colin also states "Most of the observed badges are from World War I (1914-1918). That observation ties in with my own research on these items (but I had only looked into half a dozen or so).
Some people thought that old soldiers (or family members?) had taken their badges to Paul Ysart in the 1930s and asked for them to be encased in a weight. Nice thought, but probably not the case. In his book, Colin Mahoney states: "Paul's son, Salvador, remembers his father bringing home a box filled with medals, leading to speculation that the badge weights were yet another form of experimentation ...".