The Rohirrim and Simirillion both give songs and phrases that seem to pertain to certain dieties. In fact, these "gods" are the patron Valar of these races. I don't mean to presume, but I would think that the hobbits would have adopted some beliefs from the Arnor kings at Evendim, and the rest from the secular-ish Rohirrim when they lived in the Gap. This is probably a mixture of earth mythology and lore, Numenorean fath, and Middle-folk patronage.
PS: (What about "Scouring of the Shire"? In that chapter, it clearly mentions the sand pits that the Big Men and Saruman are buried in, as well as burial mounds for the fallen militiamen at the battle)
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Horseman of the plains
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