Since zinc has an extra proton that adds on to its amu, shouldn't the zinc atom weigh more than the copper atom?
The site is down now, so I can't see what they said, but I suspect this has to do with the difference between atomic mass and density. A zinc atom, as you have correctly stated, will weigh more than a copper atom. However, because the atoms pack differently in zinc metal than in copper metal, the bulk zinc metal is actually less dense than the bulk copper metal. So one cubic centimeter (or one penny) of zinc will weigh less than one of copper. The density of copper is 8.96g/mL, while that of zinc is 7.14g/mL.