So the weight based shipping rate would only apply to shipping to the US?
The shipping country is stored in a session variable named "eCartCheckoutForm_shipping_country".
In your shipping rules, you would need to add an additional trigger for:
Based on Session Variable value
you would need to use the session variable 'eCartCheckoutForm_shipping_country" "=" a value of "US" for the wight based rules.
and create other shipping rules for the other countries, using the eCartCheckoutForm_shipping_country session variable as the trigger.