From the Super Mario Wiki, the Mario encyclopedia
This Toad is first found in the foyer of Peach's Castle shortly after the Paper Toads in the area are rescued, bragging about how lugging his sack around has made him physically stronger. When he notices that he is short one Mushroom, Mario decides to give him a Mushroom of his own. Delivery Toad thanks him by giving him a 1-Up Mushroom in return.
Delivery Toad later visits the Lakitu Info Center location in Doop Doop Dunes after the requisite Paper Toads in the area are rescued to give Mario and co the paper trampoline, as well as Trio Kite. He then visits the Lakitu Info Center location in Mount Brrr after the requisite Paper Toads in the area are rescued to give Mario and co Trio Whirligig.
As Mario, Luigi, Paper Mario, and Paper Princess Peach glide down from Bowser's Castle, Delivery Toad is briefly seen pausing his delivery to watch them.