Many of the plants won't be anywhere near rocks.
Googling terms like "solder aquarium plant weights" brings up mostly people who are guessing, plus a handful of people who say they've done it without problems. Though I did find one person who claims he did it and it instantly killed his whole tank...
Clearly you'd want to use solder without flux. The next question is, what alloy? Of the people who claimed they have done it successfully, it seems there's a divide between classic lead solder and lead free.
I realize I'm probably making a big deal out of a few bucks, but it kills me to pay 5 - 10 times more for something just because it's been repackaged for a specific hobby. Yes, plant weights are $2.50 for 12, which is cheap, but solder is a fraction of the price and I already have pounds of it in different flavors.