As promised and by request, here's another interesting comic strip featuring Weary Willie and Tired Tim, in which we meet their nephews - Little Willy and Tiny Tim. It appeared on the front cover of The Wonder dated 9th June 1898. The Wonder would later become the Funny Wonder, which in turn would last until 1942. Tom Browne, famous creator of the fat 'n' thin tramp duo, is the illustrator.
This strip is one of 150 that can be found in Denis Gifford's excellent 1976 book Victorian Comics. If you haven't yet got a copy I highly recommend you do so.