Coming of Age for Hobbits:

by Varda-(Valar)
Dec. 5, 2001

    Hobbits come of age at thirty-three, after having gone through the
irresponsible tweens (the twenties between childhood and 33).  One reason for the huge double birthday party for Bilbo and Frodo, is that it is Frodo's coming of age.

Reference: The Fellowship of the Ring Chapter One "A Long Expected Party"