What does LOTR say about hobbit longevity?
The prologue to The Fellowship of the Ring section 3, "Of the Ordering of the Shire" says:
Sixty years had passed since he set out on his memorable journey, and he was old even for Hobbits, who reached a hundred as often as not; but much evidently still remained of the considerable wealth he had brought back.
So apparently half the Hobbits who died of old age died before age one hundred and half after age one hundred. The Old Took lived to be one hundred and thirty, which is one point three times the median age of one hundred. Assuming that a Hobbit aged one hundred would be roughly equivalent to a Human aged sixty, or seventy, or eighty; a Human who was one point three times as old would be seventy eight, or ninety one, or one hundred and four.
In Humans a supercentenarian is defined as someone living to be at least one hundred and ten years old, which is relatively much older - compared to ages of sixty, seventy, or eighty - than the Old Took's one hundred and thirty years is compared to the Hobbit median lifespan of of one hundred.
Jeanne Calment (1875-1997), who lived to be one hundred twenty two, lived two point zero three three times as long as sixty years, one point seven four times as long as seventy years, and one point five two five times as long as eighty years.
It is quite possible that Tolkien knew true or false stories about people living to be supercentenarians so possibly he made the Old Took exceed the median Hobbit lifespan by such a comparatively small proportion to allow for the relatively small size of the Hobbit population which would make exceptional Hobbits much fewer than equally exceptional humans.
I suppose that there is no need to state the obvious and say that Gerontology is the study of old age and aging, comings from Greek geron (old man) and logia (study of), and that Gerontius is a Latin name, a Latinized Greek word meaning "old man" and that there are several persons named Gerontius in history, and so Tolkien was making a joke by naming The Old Took Gerontius.
For more information about Hobbit ages and lifespans, see: