What is weak soft wheat flour? What would I look for in the grocery store?

You can also make an imitation by substituting 3/4c.=2 Tb. all purpose flour and 2 Tb. cornstarch per cup of cake flour. The cornstarch is gluten free.

I'd echo what Smaug wrote—it's cake flour or pastry flour. With that said, all-purpose works for this recipe as well if you already have it on hand. (You'll have a slightly less light, tender crumb, but it'll still be delicious.)

Flour with a low gluten content- you want cake flour (it will be labeled as such- usually comes in a box) for this.