Peanut Butter Blossoms

I was making some peanut butter blossoms and they are baking too thin. Can any one help me with this? This is the recipe I used: 1 cup sugar; 1 cup brown sugar; 1 cup oleo; 1 cup peanut butter; 2 eggs; 1/4 cup milk; 2 teaspoons vanilla; 3 1/2 cups flour; 2 teaspoons baking soda; 1 teaspoon salt. In making this I doubled the recipe above. Cook in a 375 degree oven. I had the dough in the frig. When putting on a cookie sheet roll in balls on an ungreased sheet and cook 10-12 min. I had to cook the full 12 minutes to be done. After cooking immediately press a chocolate kiss or star into center.
Instead of being thicker they are real thin and the kiss looks funny on a real thin cookie. I have used this rescipe several times before and not had this problem. Not sure on what I am doing wrong. Is it that the do is cold? Oven too hot? I ws using 2 not stick cookie sheets and 1 silver tray that was not nonstick. It came out the same on both tpe of sheets. Please Help and thanks!

The brand of of butter I used was Imperial in Sticks.

I have over half the dough left is there any thing I can do to fix what is left?