I suspect they would not suffer from many of the diseases that the "big folk"
suffer from. There are not a lot of childbirth deaths in the genealogies
in the back of LOTR, nor do many Hobbits die in childhood. This seems to
indicate either a hardy group or one that was not exposed much to infectious
disease (except for extraordinary events like the great plague).
I agree with Dame Ioreth that Hobbit medicine was probably focused on herbs and
midwifery (probably a big demand for the latter, what with those huge Hobbit
families!). I also think that Hobbit medical care would have centered on
home remedies (passed down in that famous store of Hobbit wisdom that ordinary
humans had long since forgotten), with perhaps a more knowldegeable person
called in if the remedies proved ineffective. Hobbits would also need to
know how to handle accidental injuries -- set bones, stitch cuts,
etc.
With caffeine, all things are possible.
The pity of Bilbo could screw up the fate of many.
