>>1112090I use two 8lb Mushroom Anchor Running off the front and back of the kayak, attached via overhand loops to carabiners.
I have a pretty big Advanced Anglers 120 Fishing Kayak, I just use polyprene rope because of how thin it is, and just shove the line under my seat.
Pic related.
The Main thing to prevent getting blown around in the wind is to anchor in front, and behind the kayak, and pulling them tight.
It could also be you are not using enough weight.