What shipping method are you using to get the UPS option? Is it one of your Base Plus shipping methods, or is it from the real-time UPS shipping quotes feature?
For Base Plus Shipping there are per-product shipping charges configured in the product info, plus an optional base amount configured in the Commerce Setup -> Shipping menu.
When you enable the handling charge feature, you can enable per-product handling charges, as well as use the global handling charge formula in Commerce Setup -> Shipping.