Here is an IDEA to consider. I have done this. It can be applied to nesting bowl also.People who use the dollar tree dog bowls as nesting bowls. Do you weigh them down?
The above is an Inexpensive bird bath. It is made of light hollow plastic. 2 advantages; is le$$ cash, and lasts a long time. Disadvantage; falls over very easily.
My solution; I filled the bottom pedestal portion with concrete cement. Now the birdbath is heavy, and does not blow over.
So now to this.
2 things can be done with this.
Turn upside down, and fill with concrete cement. Another option is a mixture of sand and Plaster of Paris for a quicker setting.
Now for the second part; Use as a weighted down bowl, or after cement cures, separate plastic from cement, and use cement as bowl. It will have texture of sand of cement.
For anyone consider going this route, I suggest the option of using Mortar Mix Over Concrete mix. The concrete mix has stones up to size of chestnuts in mix. Sometimes less than IDEAL to work with for small size items.