Looking at this C# code:
byte x = 1;
byte y = 2;
byte z = x + y; // ERROR: Cannot implicitly convert type \'int\' to \'byte\'
The result of
I remember once reading something from Jon Skeet (can't find it now, I'll keep looking) about how byte doesn't actually overload the + operator. In fact, when adding two bytes like in your sample, each byte is actually being implicitly converted to an int. The result of that is obviously an int. Now as to WHY this was designed this way, I'll wait for Jon Skeet himself to post :)
EDIT: Found it! Great info about this very topic here.