  Austin's moving knife procedure is used to divide a cake equitably between
two agents: each agent believes that they received exactly half of the cake.
This short note deals with the case when the two agents have unequal (rational)
entitlements to the cake and seek a weighted equitable division -- one where
each agent believes that they received exactly the share that they are entitled
to -- and also minimizes the number of connected components that each agent
receives. First, we adapt Austin's moving knife procedure to produce a weighted
equitable division of a circular cake that gives exactly one connected piece to
each agent (recovering a result of Shishido and Zeng's). Next, we use it to
produce a weighted equitable division of a star graph cake that gives at most
two connected pieces to each agent -- and show that this bound on the number of
connected pieces is tight.
