Does this imply that four yards worth is a statement of possession, that four yards collectively own a worth?
What is a worth, of which this mutiplicity of yards have taken possession?
When I buy ten dollars worth of fuel, for my very small motor at current prices, do the ten dollars likewise take possession of the fuel, or do I take possession of the amount of fuel that ten dollars buys?
Four yards worth, as is anything else worth, is an expression of quantity
No, "four yards worth" is a statement of quantity, it's bad grammar, but it still means: the amount of four yards, no possession is implied.