Shipping is priced in tiers, not on a smooth curve, so the cost of a parcel jumps at fixed weight breaks rather than rising gradually. The parcel that costs the most is the one that crosses a break by an ounce. These 11 guides give the rates at each tier and name the service that wins there.
Weigh the parcel packed, with the box, the void fill and the tape on the scale. Carriers bill the weight they measure, not the weight of the contents, and a reweigh adjustment lands on the account weeks after the label was bought.
I'd Ship That prints discounted USPS and UPS labels. If you know the service already and only need its full table, use the rate guides; if you want the packing decision for a specific item, use the item guides.