One more thing - Use 1/32" balsa instead of the 1/16" you mentioned. It will give you more than enough strength. It's not the thickness of the balsa that gives strength, it's the completeness of the bond of the foam to the balsa.
That depends what you are building and loads it is expected to withstand. A good bond with foam will help prevent the skin from buckling under compressive loads, but it is the thickness of the balsa and it's density that withstands compressive loading.