The Up Arrow is an important item found in the game Paper Mario: The Thousand-Year Door that is very valuable.
Merlon can only upgrade Mario's partners once in the game until the end of Chapter 5. When Mario goes outside Merlon's house, Merlon will tell him of a dream he had. In his dream, Mario used Bobbery to access a treasure in Hooktail Castle. In Hooktail's Castle, there is a crack in the wall that can be blown up by Bobbery. Once the wall is blown up, Mario can find a treasure chest in an open room. The treasure chest contains the Up Arrow.
When Mario returns to Merlon, Merlon wonders what it means. Then, Merlon tries flying up and sees what happens. Merlon discovers an Ultra Stone that he bought from a Flea Market long ago, put in his attic and forgot about. With the Ultra Stone, Merlon can now upgrade Mario's partners twice.