downhill adv.

"in a descending direction, from a higher to a lower place, degree, or condition," late Old English shortened form of Old English ofdune "downwards," originally of dune "off from (the) hill," from dune "from the hill," dative of dun "hill" (see down (n.2)). The "hill" word is general in Germanic, but this sense development is peculiar to English. As a preposition, "in a descending direction upon or along,"  from late 14c.

To be down on "express disapproval of" is by 1851. Down home is from 1828 as "in one's home region," as an adjective phrase meaning "unpretentious" by 1931, American English. Down the hatch as a toast is from 1931. Down to the wire is 1901, from horse-racing.

Down Under "Australia and New Zealand" attested from 1886; Down East "Maine" is from 1825; Down South "in the Southern states of the U.S." is attested by 1834. Down the road "in the future" is by 1964, U.S. colloquial. Down-to-earth "everyday, ordinary, realistic" is by 1932.

Old English hyll "hill," from Proto-Germanic *hulni- (source also of Middle Dutch hille, Low German hull "hill," Old Norse hallr "stone," Gothic hallus "rock," Old Norse holmr "islet in a bay," Old English holm "rising land, island"), from PIE root *kel- (2) "to be prominent; hill." Formerly including mountains.

In Great Britain heights under 2,000 feet are generally called hills; 'mountain' being confined to the greater elevations of the Lake District, of North Wales, and of the Scottish Highlands; but, in India, ranges of 5,000 and even 10,000 feet are commonly called 'hills,' in contrast with the Himalaya Mountains, many peaks of which rise beyond 20,000 feet. [OED]

The term mountain is very loosely used. It commonly means any unusual elevation. In New England and central New York, elevations of from one to two thousand feet are called hills, but on the plains of Texas, a hill of a few hundred feet is called a mountain. [Ralph S. Tarr, "Elementary Geology," Macmillan, 1903]

Despite the differences in defining mountain systems, Penck (1896), Supan (1911) and Obst (1914) agreed that the distinction between hills, mountains, and mountain systems according to areal extent or height is not a suitable classification. ["Geographic Information Science and Mountain Geomorphology," 2004]

 Figurative phrase over the hill "past one's prime" is recorded by 1950. Expression old as the hills is recorded by 1819, perhaps echoing Job xv.7. Earlier form old as the hills and the valleys is attested by 1808:

And this is no "new morality." It is morality as old as the hills and the valleys. It is a morality which must be adopted; or, we must confess that there are certain political evils greater than that of seeing one's country conquered. [Cobbett's Weekly Political Register, Feb. 6, 1808]

Cobbett's also had, on April 11, 1818:

However, thus it always is: "those whom God intends to destroy, he first makes foolish," which is a saying as old as the hills between Everly and Marlborough.