The Per Unit perweightunit shipping module takes the:
(products_weight * quantity ordered) * Unit Rate

to create the shipping charge for the product ...

If the Unit Rate for the 3 zones were proportional, US being 1, Canada being 1.25 and the Rest of the World being 1.75 ... as an example, then a Product with Product Weight of 3 would be:

Quantity 1
US = (3 * 1) * 1 = $3.00
Canada: (3 * 1) * 1.25 = $3.75
World: (3 * 1) * 1.75 = $5.25

Quantity 2
US = (3 * 2) * 1 = $6.00
Canada: (3 * 2) * 1.25 = $7.50
World: (3 * 2) * 1.75 = $10.50

This can be accomplished by cloning the Per Unit perweightunit shipping module for the 3 zones and then setting the weight on the products to be the shipping cost to the US for each product ...