I live in a windy area too, and I have had both experiences: a heavy wooden bench that never moved, and a lightweight aluminum bench that flipped twice before I anchored it. So the honest answer is: it depends far more on the bench design, weight, and placement than on the simple fact that it is windy.
Wind tips a bench over when it hits a large vertical surface. The backrest is the biggest problem because it acts like a sail. If the bench is light and has a tall, solid back, a strong gust from behind can push the top of the backrest, lift the front legs, and tip the whole thing over. If the bench is low, heavy, and has an open-slat back, the wind passes through more easily and the weight keeps the base planted.
A good rule of thumb: if you can lift one end of the bench with one hand without straining, treat it as a tip-over risk in a windy area. Benches under about 30 pounds are usually the ones that get blown around. Benches over 50 or 60 pounds rarely flip in normal windy weather, but they can still shift or get pushed around in storm gusts over 50 to 60 mph.
If you are choosing a bench, look for solid materials like teak, acacia, eucalyptus, powder-coated steel, wrought iron, or heavy recycled plastic. Avoid hollow aluminum, thin tubular frames, and cheap plastic unless you plan to anchor them. A lower back and a wider stance also help. Benches with open slats are better than solid-back benches because they let wind through instead of catching it.
If you already have a bench that might tip, you do not have to replace it. The easiest fix is to weigh it down. You can add sandbags or steel weight plates to the underside of the seat, but make sure they are attached securely and do not look messy. On a lawn or gravel area, use ground anchors, tent-style stakes, or spiral dog stakes and connect them to the legs with short cables or straps. On a patio, you can bolt the bench to concrete or pavers with small L-brackets. Even a couple of heavy planters placed against the legs can block the wind from getting under the bench and reduce movement.
Placement matters just as much as the bench itself. If possible, move the bench against the side of the house, a fence, or a dense hedge. This cuts down the wind reaching the backrest. If the bench is sitting in the middle of an open yard or on a hilltop, it will take the full force of the wind. A windbreak made of shrubs, a trellis with climbing plants, or a decorative screen can make a noticeable difference.
During storms or very strong wind events, the safest option is to store lightweight benches indoors or in a shed, or at least fold them and lay them flat. A bench lying face down is almost impossible to tip over because the wind has nothing to push against.
So in short: no, a good-quality outdoor bench will not tip over easily in most windy areas, but a light or poorly placed bench might. If you want to keep a bench outside in a windy area, choose something heavy with an open back, and anchor it if you can. That combination solves the problem in almost every condition.