Also I imagine a Hobbit's calorie requirements are substantially lower than a man 3 times their size. They're no less intelligent (indeed they are shown to be p

Also I imagine a Hobbit's calorie requirements are substantially lower than a man 3 times their size. They're no less intelligent (indeed they are shown to be particularly clever), they have access to draft animals and basic machines, so their agricultural productivity is likely still high. This should allow for substantially greater surpluses even before we invoke magic.