The colloquial phrase to sweat the small stuff means to worry about trivial, insignificant matters.

This phrase usually occurs as don’t sweat the small stuff, said as reproof or consolation.

The phrase to sweat the small stuff occurs, for example, in the review of Everybody Wants Some!! (2016), a teen-comedy film written and directed by the U.S. film director, producer and screenwriter Richard Linklater (born 1960)—review by Charlotte O’Sullivan, published in the London Evening Standard (London, England) of Friday 13^th May 2016:

Richard Linklater is fascinated by dramas in which the stakes are “really low”. His genius lies in making us sweat the small stuff.

The earliest occurrences of the phrase to sweat the small stuff that I have found indicate that it originated in U.S. teenagers’ slang—these early occurrences are as follows, in chronological order:

1-: From The Atlanta Constitution (Atlanta, Georgia) of Saturday 17^th August 1957:

TEEN-TALK
Hipster Knows Top 10 Sides

Atlanta teen-ager Aleck Janoulis defines a “hipster” as “anyone who can tell you the top 10 tunes of the country in order. He is able to tell anyone the number of a particular side (record) on a local organ grinder (jukebox) without looking for it. A true hipster must be in the know (in style) with the latest togs (clothes).”
A “cube” or “3-D square” is just the antonym of a hipster, Aleck explained. “The poor bugger (England’s term for a square) thinks the tune title ‘Dark Moon’ means the side is about an eclipse. He doesn’t catch (know about) the stripes (Ivy League), and is still walking around in pink and black.
“A 3-D square,” he continued, “doesn’t even dig a West Coast bop joke.”
Aleck submitted the following teen-terms:
MR. MONEYBAGS—Elvis.
NOD—Sleep.
OUTEST—The best.
PUZZLES—English grammar tests.
STOMPERS—Shoes.
STROLLER, WHEELS—A car.
TICKS—Minutes.
Other definitions submitted this week include:
GO POUND SAND—Drop dead.
ONE ON THE CITY—Glass of water.
SISSY STICKS—Soda straws.
(Submitted by Wayne Wright, Atlanta.)
DON’T SWEAT THE SMALL STUFF—Don’t worry about it.
BIG WHEEL—Important person.
(Submitted by Shirley Mell, Decatur.)

2-: From Tiger Tabs, “the latest tid-bits about the students, as well as the faculty, of S.V.H.S.” [i.e., Spring Valley High School], published in The Journal-News (Nyack, New York) of Wednesday 20^th May 1959:

Junior Roger Cohen is running for vice-president of next year’s G.O. officers on the 4-Volts party. He is a member of French Club, S.S.C., is vice-president of the Key Club, president of the Latin Club, president of HR 79, a G.O. rep, and a Junior rep.
“Don’t sweat the small stuff” is a well-used expression of Roger’s.

3-: From the column Tempus Puget, by Lenny Anderson, published in The Seattle Daily Times (Seattle, Washington) of Wednesday 11^th November 1959:

Teen-Age Slang; A Warning
Upon asking a group of Lincoln High School pupils to list and translate a few slang expressions now in use among the younger set, we received a mild rebuke, expressed with the patient understanding many youngsters have for their seniors.
New expressions have sprung up, we were told, but most of those who write about them leave the impression that high-school youngsters always speak this jargon. This is not true, our informants continued. The slang expressions are used rather sparingly. With that preface, here are a few examples:
Rank: To knock something or someone.
Rink: A character with greasy hair and low-slung pants.
What’s the skinney?: What’s the deal?
Fuz: Policeman.
Cool it: Take it easy.
Pad: House.
Grub: A bum or slob.
Bug out: To leave.
Don’t sweat the small stuff: Don’t let minor troubles bother you.
That’s all. I have to bug out. And if these definitions don’t jibe exactly with yours, Jack, cool it; don’t sweat the small stuff.

4-: From the column Gatorville Gababout, by Lori Gagner, published in the Daytona Beach Sunday News-Journal (Daytona Beach, Florida) of Sunday 31^st January 1960:

MOVE OVER ALBERT—As first semester grades move in on the home front this coming week, old faithful mascot, some students will probably need a new home . . . your gator pen or a dog house, it’s all the same. As of yesterday, exams are in the past and the last grade has been made. Whether negative or affirmative, if nothing else can be said about finals, at least they are over for another four months.
“We don’t sweat the small stuff” or “don’t sweat it” is the verbal attitude towards grades which officially will be sent to parents sometime this week. But actions speak louder than words, and as students pounce upon the mailman each day until the telltale letter arrives, it shows . . . students DO sweat the bad news grades.