I’d treat it as two problems: stopping the wobble and stopping water from sitting under the legs. First, empty the furniture and put it where you actually want it; moving a table after leveling wastes time. Check the patio with a straightedge or spirit level to find high and low spots. Then inspect the piece: many urban outdoor chairs and tables have adjustable glides or feet. If so, extend the low leg a little at a time until the frame is stable. Don’t crank one leg way out—it stresses the joints.
If the feet aren’t adjustable, use outdoor-rated shims. Rubber or composite shims are better than wood scraps because they grip and don’t rot. For a small gap, stack no more than two shims; for bigger gaps, use a solid spacer such as a cut rubber paver pad or a hard plastic furniture pad under the leg, then fine-tune with a thin shim. Put shims under the leg or frame foot, not under a loose crossbar, and check that at least three legs bear weight evenly.
On concrete or stone, add non-marking rubber pads under metal legs to reduce slipping and scratching. On wet patios, avoid trapping water: use pads that let water drain, and clear debris from the low corner. If the furniture is heavy or used often, consider bolt-on adjustable feet or a small treated plywood base with drainage holes—but check rental or building rules first. For umbrellas and tall pieces, secure them or add weight low down; leveling alone won’t stop wind tip-over. Finally, sit or lean on each piece and rock it. If it still moves, re-check the shim placement and try rotating the furniture slightly. A level patio isn’t always necessary—stable, draining, and safe is the real goal.