you will need a seperatre rule for each wight range.
the shipping country is stored in a session named:
eCartCheckoutForm_shipping_country
so your rule would use a combination of Session Variable Value and subtotal for any column for th triggers. For example:
"based on session variable value"
if the session variable "eCartCheckoutForm_shipping_country" has a value of "UK"
AND
"based on subtotal for any column"
If the subtotal for column "TotalWeight" is ">" "0"
AND
"based on subtotal for any column"
If the subtotal for column "TotalWeight" is "<=" "1"
Flat rate change of 5.99
the other rules will be similar, just change the weight range values and the flat rate.