Well I just think it is a scaling up of the traditional 21 coming of age to fit the significantly longer Hobbit life spans. Centenarians were a rarity when Tolkien was writing The Hobbit and LOTR.
http://healthlongevity.blogspot.com/...cord-high.html
But for Hobbits a hundred was relatively unremarkable and Bilbo and the old Took surpass even today's oldest of the old by a decade. Hobbits seem to have approximately a life span up to 50% longer than the human traditional threescore years and ten
This gives an extended period for Hobbit youngsters before they were expected to take on full adult responsibilities. Sam is clearly at an age when he is expected to settle down whereas Pippin and Merry aren't quite . They may of course grow slower than ordinary mortals (the secret of their tough fibre?) and presumably female hobbits had correspondingly longer childbearing years (poor old Rosie). Don't have the appendices on me to check just now. I think the ages went through a few variants in home and it may be, prosaically that the ages were so Tolkien oculd make his "gross" joke.