Here is another update.
First, Daisy was right, the old weak stem won't change its original thickness.
However, it is still worth it to graft a seedling even on a weak root stock.
This photo shows the plant grafted on May 24 (left), June 3 (right), and the same batch of seedlings on their own roots in the small green pot in the middle.
By the way, the initial graft on May 19 was knocked off, probably by a bird.
The biggest growth was my second attempt. It's amazing how much it has gown in over one month. Sorry for the wrong focus point in the photo.