PHB Barding Rules for Mounts/Mastiffs

The barding rules in the phb for mastiffs doesn't make sense. The rules say, "Barding is armor designed for a mount. Any type of armor on the Armor table in this chapter can be purchased as barding. The cost is four times the normal cost, and it weighs twice as much."
I think this assumes the barding is for a large creature, like a horse. What about for a mastiff, which is a medium creature? Would a chain shirt for a mastiff weigh twice as much, and somehow be four times as hard (and therefore four time the cost) to make?

Shouldn't size be taken into account?

What is the ruling, and what are your thoughts?