No, you're not charged for both. It's one or the other. Either weight or dimensional weight. So, if you have a 1 foot cube that weighs 50 pounds, you're charged 50 pounds. If it's a 4 foot cube that weighs 5 pounds, you'll be charged the dimensional weight (probably 30-40 pounds).

Trust me, I've found this out the hard way on next day air shipments. You think it's going to be $50, and get a bill for $150!