I have to have very heavy pots too, and sometimes that's not enough for wind gusts above 30 mph. On almost any day over the summer, a storm can pop up that will rearrange pots if they aren't prepared. Using clay pots instead of plastic helps with that, but they become too expensive when they are bigger than about a gallon size.
If a heavy pot full of heavy soil isn't enough, propping them with bricks around the outside helps to make sure they stay where I put them. Ground dirt is usually heavy enough to provide enough ballast, but not always.
This is why I'm such a huge fan of hanging pots.
Just after repotting, some plants are in danger of coming out of the soil so I put bricks across the top of the pot in a circle, or a few smaller rocks around the base of the plant so the wind can't pull it out before it takes root in the new soil.
Bricks and rocks are too valuable to me to hide at the bottom of a pot. Sally, I bring rocks home from anywhere we go where there are rocks. I'm one of those nerds who buys rocks at a gift shop. A lot of them are on display in my mini gardens and some are in a fountain. The purchased one are inside on little shelves. If I'd known I was moving to a place with no rocks, I would have brought more than my 3 fav ones from OH. I used to go to where they were building housing developments and pick up the most beautiful rocks and take them home. When my gramma passed a few yrs ago, I found a little copper bowl where she had put the rocks I gave her when I was a kid. Sorry, I'm babbling about rocks.