chicken wire is sharp and adds a surprising amount of weight. While I love plaster gauze, again it's heavier than you might realize. Luckily, these heads are perfect candidates for good ol' paper mache.
I'd use corrugated cardboard for the saucer portion, a tiny bit of paper mache on the rims & raised edges and it's pretty much done.
The cups I'd go with the old 'cover a balloon or ball in paper mache' method. BONUS: You need two half circles to create two cups, so you can actually get both cups out of one beach ball paper mache session. More cardboard to fill out the cup handles and close the tops and the structure is done.
GENERAL NOTE ON MAKING HEADS:
This is a head, which should be scaled to the character (within reason) not your natural head. Often people start with the measurements of their own head then don't like the results because the proportions are all wrong. You can comfortably wear something that extends 6" beyond your shoulder width without too much issue. Bigger than that you need a handler.
This is not a hat, therefore the weight should be resting on your shoulders. You might need a headband or padding inside it to secure it from bobbling or so that your eye holes turn with your face.