Stones are like the ultimate go-to symbol for virtually every poet, artist, philosopher—you name it. The speaker uses it in "maggie and milly and molly and may" to symbolize the lonely world we live in that can feel both big and small at the same time. May holds it in her hand and gets all philosophical on us because, what else is there to do when you're looking at a stone?
Lines 9-10: The smooth stone reminds may that the way we feel about the world depends on how we perceive it. It can seem small when you feel like you're on top of things and then it can feel large when it seems like stuff is out of your reach. So the stone (and world) are really both things: big and small, lonely and within reach.