I won't call mine authoritative, but I know something of this.

Enumerated types are really just integer fields with defined constants associated in name and in incremental value. If you use them as just an enumerated type they should default to 1 byte in size, unless you have more than 255 elements. In a set, however, each element represents a bit toggle ... and so you need to divide your elements by 8 and round up (minimum of 1).

Thus an enumerated type of 16 elements is 1 byte in size, but a set of that type is 2 bytes in size.

Hope that helps.