I just use plants that can handle floating like elodea, wisteria, and hornwort. All three are dirt cheap, grow like weeds (because they are weeds), and can live just fine uprooted. Frog behavior is a night and day difference with the plants in there.
If you’re hell-bent on weighing plants down, river stones from the craft store are a good option. You can use hot glue also. I have a java fern that is 10 years old and has been hot glued to a stone since day one.