There are 4 basic things I always try to do:
Melt the butter!
Use more brown sugar than white. For example, the normal recipe calls for 3/4 cup white sugar and 3/4 brown sugar...Alter this and use 1 cup b. sugar and 1/2 cup w. sugar!
I never have issues with my cookies coming on paper thin anymore! They are much more appealing, and with the alteration of more Brown sugar, I think they taste better too! I hope these tricks work for you, leave me a comment and let me know!
*Oh on a funny note, I stored some of these cookies with some of the whoopie cakes, and the cookies were SO soft, because the cakes were super soft. I guess this compares to storing your cookies with a slice of bread. It totally worked*