Ah, that's simple.
In the settings of each product:
Go to Seller Admin>View/Edit/Delete Products:
Select an existing shippable product of yours and click Edit;
On the first screen, if Shipping/Buyer's Address is not checked there, tick that box;
Click Next until you reach the Shipping Options screen;
Enter a Weight equal to the flat rate you want to charge per unit for that product;
Package type and Capacity won't matter here;
Click Next until you can Submit settings;
Repeat this for all your tangible goods;
When adding new shippable products, remember to enable Shipping/Buyer's Address and enter its Weight as the rate you want to charge.
Go to Seller Admin > Cart Shipping Settings and set up the following:
Shipping Origin: select your country and enter your zipcode (if you're outside the US, just enter any 5-digit number);
Shipping Destinations: if you will only ship to certain countries, select them in the list, or otherwise select nothing for Worldwide shipping;
Leave all other settings blank or 0.00;
Click Next to save settings and proceed to the Shipping Rules screen.
In the Existing Shipping Rules menu, select and Delete any Rules you may have there.
Set up your first Shipping Rule for Domestic shipping:
Shipping Rate Calculator: Price per unit weight;
Shipping Amount: 1.00;
Country: Select your country;
Click Submit to save the Rule.
If you will ship Internationally at a different rate:
Shipping Rate Calculator: Price per unit weight;
Shipping Amount: enter a multiplier of your Domestic rates (e.g., if Int'l rates are twice your Domestic rates, enter a rate of 2.00 here);
Country: All Countries (i.e. Rest of the World);
Click Submit to save the Rule.
Click Back to Admin, and you're done!
