Looking at your screenshots, I arrive to the same conclusion as Jerome:
For what I saw, you products does not have any size and we don't know anything about your UPS configuration.
To which you replied about the weight of the product being filled in. But Jerome talked about the size (ie the width, height, length) of your product which seems to have been left empty while they are necessary for UPS the calculate the shipping fees automatically.
so that's probably what you're missing. But it could also be something else in your shipping method since you didn't provide a screenshot of all the options of the UPS shipping method.