That's a great question! A wobbly or tipping bin on a brick patio or walkway is a real nuisance. The best method depends on whether you need a permanent or temporary fix and your brick type (e.g., smooth pavers vs. rough texture).
For a heavy, non-movable solution, using a weighted base is highly effective. You can place a heavy concrete paver or a custom-cut stone slab inside the bottom of the bin liner. This lowers the center of gravity. Alternatively, you can create a permanent anchor point by drilling into the mortar joint (not the brick itself, as it can crack) and installing a concrete screw or sleeve anchor. Then, use a sturdy nylon strap, bungee cord, or a short chain to loop around the bin's handle or body and secure it to the anchor.
If drilling isn't an option, high-strength construction adhesive like Liquid Nails or a outdoor-rated epoxy can be used to glue a mounting bracket or a flat plate to the brick. Attach the bin to this bracket. For a completely non-destructive, temporary hold, consider using a freestanding weighted bin enclosure or a specially designed outdoor bin anchor kit that uses ground spikes or sandbags.
The key is to assess your specific bricks and choose a method that balances security with your need for access and cleanliness. Always ensure the bin can still be easily emptied by service personnel if needed.