I used to do a lot of kayaking. Every weekend plus two evenings a week. And kayaking holidays. I’ve kayaked from size 14 to size 20. (Well, the clothes said 20 but they were quite tight).
There are different types of kayaks and different types of kayaking. I’d suggest finding a club so you can try a few. Or try a kayaking taster activity at Plas Menai or similar.
If your size is a concern, you may prefer a sit on top kayak. They are very (comparatively) stable. You will wobble getting on and off. Don’t worry, that is normal no matter what your weight and size. This can be used for sea kayaking (less common in the UK) and flat water kayaking (a lake etc). Not white water, you will fall off because you can’t brace yourself against the boat.
Enclosed kayaks. There are different types.
Touring kayaks are used on mostly flat water (they can handle little waves so saying flat water can be misleading). Lakes, rivers, estuaries. Quite versatile.
Racing kayaks. Also referred to as tippy boats. Great fun! You will fall in. And laugh about it unless you are actually racing.
White water kayaking is great fun. The hull is very flat which makes it hard to paddle if the water is moving under you but also gives you more stability.
What to wear - you don’t need a wetsuit. You need something warm that won’t be heavy if when it gets wet. So don’t wear a fleece. Wear legs and a running top. If you go white water kayaking, you actually want a dry suit or dry suit top and wet suit bottoms.
You can easily go kayaking!