I have a lot of trouble with plants blowing over too. Are you able to use something unobtrusive like fishing line to secure them to something?

If you can devote space inside pots, a rock at the bottom can help, as it lowers the center of gravity, as long as it doesn't block the drain hole(s.)

If weight is a concern, different pot shape might be a better avenue to explore vs. heavier pots of a traditional shape. If you are looking for new pots, those that are low and wide would be more stable than the traditional "flower pot" shape with its' high center of gravity. A couple of my pots used to be the lid of the plastic package holding a bought cake. These have never been blown over. Although they weigh only a couple ounces empty, their shape is very stable with a very low center of gravity because the sides are only slightly sloped/flared out.

A heavy cache pot can help keep a plant upright, but if rain hits your balcony, (and fills the pot(s,) that could cause more problems than it's worth, and has the weight issue.

You could fashion some wooden (or metal of some type?) supports cut to just the right size to wedge (or maybe glue) between the pot rim(s) and the floor, to make the overall design exactly the opposite, with the wide part at the bottom. This shape is very hard to tip vs. the ease of tipping the traditional shape.

Square pots are also more stable than round :)

My balcony is very windy as it's on the 42nd floor. I mostly use plastic self-watering troughs that are low so the plants have room to grow before they reach the top of the balcony partition. Once foliage surpasses the balcony, the battle with the wind is futile.

I also use oversized insulated plastic pots that, like the troughs, are lightweight and hold lots of dirt, giving the plants lots of room to grow roots to secure the plants in the wind. Weighted down with planting medium and water, the pots are too heavy to budge in the wind but light enough to not worry about overburdening the concrete slab underneath.

The troughs are a rectangle planter and a square planter combined into one planter to fit my 54"w balcony snugly, with less than a 1/2" to spare. I fill them with a mix designed for self watering containers, which is very lightweight. Wind dries out plants, and having a 'self-watering' feature, essentially a water tank to fill, helps, particularly at the height of summer when we get the most sun, from 1:00 to sunset.

I've gone the fishing line route, but I don't recommend that. Yes, fishing lines helps secure plants and they grow vigorously, generally without falling over. However, once the wind picks up, the fishing line acts line a fine blade cutting stems and branches.

I know this is an older forum, but I just came across this and thought I would chime in. Hope it helps someone.

Totally agree about fishing line against the actual plants, and good additional info in general. Different circumstances/locations and diff plants require diff measures! Fishing line, I've only used it to lash pots in place, and to let vines grow on. The occasional vine stem has gotten broken by being blown against the line wrong.

Wind blowing the actual plants is not usually my problem, just when it knocks pots over.

Last night we got over 5" of rain and enough wind to blow the mini blinds around inside closed windows. No actual tornado came over the house, but the sirens were blowing and stuff on shelves was jiggling. Looks like 2 out of about 100 pots did blow over sideways, but no plants seem damaged from the experience, topically anyway. I'm not sure they all appreciated getting THAT drenched.

I have just had a mesh called "Galebreaker" bolted on to the iron railings of my top floor terrace! Now I can at last grow some plants in window boxes or have some small trees in pots to look at! Many thanks to Raemoir Garden Centre, Banchory, Aberdeenshire, UK and to Databel Trading, Gembloux, Belgium for their excellent advice and work. And to the Galebreaker for their excellent product and advice!