The proverb look after the pennies and the pounds will look after themselves means if you concentrate on saving small amounts of money, you’ll soon amass a large amount.

Unlike a phrase such as a penny for your thoughts, which dates back to the early 16^th century, this saying is relatively recent, since it is first attested in the mid-18^th century as take care of the pence, and the pounds will take care of themselves, the form that was recorded in the fascicle, published in 1909, containing the words beginning with the letters O and P of the New English Dictionary—as the Oxford English Dictionary was known. The first known users of the proverb, two fathers giving advice to their respective children, attributed its coinage to various persons, thus indicating that it was new to them.

In a letter that he wrote from London on 6^th November 1747 to his son, Philip Stanhope (1732-68), who was in Germany, Philip Dormer Stanhope (1694-1773), 4^th Earl of Chesterfield, drew a parallel between saving money and saving time:

If my letters should happen to get to you, when you are sitting by the fire and doing nothing, or when you are gaping at the window, may they not be very proper flaps, to put you in mind, that you might employ your time much better? I knew, once, a very covetous, sordid fellow, who used frequently to say, “Take care of the pence; for the pounds will take care of themselves.” This was a just and sensible reflection in a miser. I recommend to you to take care of minutes; for hours will take care of themselves. I am very sure, that many people lose two or three hours every day, by not taking care of the minutes. Never think any portion of time, whatsoever, too short to be employed; something or other may always be done in it.
(from Letters written by the late right honourable Philip Dormer Stanhope, Earl of Chesterfield, to his son, Philip Stanhope (London, 1775))

In another letter, dated 5^th February 1750, Lord Chesterfield, ascribing the saying to a different person, drew the same parallel:

Young people are apt to think they have so much time before them, that they may squander what they please of it, and yet have enough left; as very great fortunes have frequently seduced people to a ruinous profusion. Fatal mistakes, always repented of, but always too late! Old Mr. Lowndes, the famous Secretary of the Treasury, in the reigns of King William, Queen Anne, and King George the First, used to say, take care of the pence, and the pounds will take care of themselves. […]
This holds equally true as to Time; and I most earnestly recommend to you the care of those minutes and quarters of hours, in the course of the day, which people think too short to deserve their attention; and yet, if summed up at the end of the year, would amount to a very considerable portion of time.
(from Letters written by the late right honourable Philip Dormer Stanhope, Earl of Chesterfield, to his son, Philip Stanhope (London, 1775))

On 12^th October 1750, in a letter that he wrote from Roscommon, in western Ireland, to his daughter, Alicia (1733-1807), who was living in Dublin, Edward Synge (1691-1762), Anglican bishop, attributed the invention of the proverb to yet a different person:

You seem to wonder that my Correspondents direct to me in Dublin – I desire my constant ones to do so, and I wish all did – Don’t you see, Mistress, that thus half-postage is sav’d. But it is too early for you to think of such things, and yet a little proper attention, to avoid unnecessary expense even in small things, is not amiss – A saying of Old Judge Daly’s is in every one’s Mouth. Take care of the pence, the pounds will take care of themselves.
(from The Synge Letters. Bishop Edward Synge to His Daughter Alicia, Roscommon to Dublin 1746-1752 (Lilliput Press, 1996), edited by Marie-Louise Legg)

(related: the penny dropped – pennies from heaven)