You would think that wouldn't you, I mean about the narrower tyres thing. Usual the converse is true.
Up a width usually lightens the wheel in my experience, obviously going from a 5 inch wide 13 to a 10 inch wide 18 theres gonna be a lot more friction.
Width/profile/size indeed.
165 is the width in mm,
the 70 is the aspect ratio, 70% of the 165,
13 is the wheel size.
Chris