Somebody update me, but I believe that physical mail and packages are delivered to a security screening facility well away from the capitol and much delayed before any delivery to the House or Senate.
You are correct. Another consideration is that, although the boxes might weigh next to nothing, FEDEX and UPS can also use “DIM Weight” to determine the cost of sending a package. This is done by computing the volume (length x width x height) of the box and using that figure charges. They do this sepcifically to avoid having to dedicate haul assets to move large amounts of air for little revenue.
Seems like I remember hearing about this when we all sent the tea bags to Washington last year. They ended up in a screening warehouse and were thrown away.