Make a test product with weight of 0.1 ... add to cart and see if you get a quote ...

Check that your USPS Web Tools User ID is entered correctly ... it is often best to cut and paste vs type it as there can be a lot of mistakes with that and it breaks ...

I would also re-add the v1.3.7.1 USPS module and REMOVE, INSTALL and Reconfigure it just to be sure that all is right in the world ...