In the colloquial phrase a spare tyre around the waistline, and its variants, the noun spare tyre denotes a roll of fat. (This noun literally denotes an extra tyre carried in a motor vehicle for emergencies.)

Incidentally, the U.S.-born British novelist Alice Campbell (1887-1976) made a character liken an obese man to “a mass of spare tyres” in The Click of the Gate, published in The People (London, England) of Sunday 21^st February 1932:

“The fellow has a waist-line, which is one up on the Baron von Sausage-skins, who is a mass of spare tyres from the feet up.”

The earliest occurrences that I have found of the phrase a spare tyre around the waistline and variants are as follows, in chronological order—first in American English, then in British English:

 

IN AMERICAN ENGLISH

 

1-: From the following advertisement for Fisher’s, “the woman’s store”, published in the Olean Evening Times (Olean, New York) of Wednesday 25^th September 1929:

If You Want to Wear the New Dresses, Now . . . Get Into
The Correct Foundation Garments

This is why . . . The girdles you have been wearing confined the hips, but they pushed the flesh up into a “spare tire” around the waist. And now the new dresses accent the waistline with a “nipped in” effect, conforming to the natural figure. Which makes the proper foundation garment the first essential to a smart wardrobe. In Fact: Don’t even try on the new dresses over your old girdle—you’ll think you can’t wear them. But, when your foundation garment is right, you’ll find the new silhouette is most becoming. So come to our Corset Shop and be properly fitted at once—before you buy your new frocks.

2-: From the following advertisement for Luckey, Platt & Co., published in the Poughkeepsie Eagle-News (Poughkeepsie, New York) of Wednesday 25^th September 1929:

Get Rid of That “Spare Tire” ’Round the Waist

The corsets they’ve been wearing confined the hips but they pushed the flesh up into a roll around the waist and since the waist line is accentuated in all the new models, it is essential to get rid of that “Spare Tire”. The best way to do if you want to wear the new dresses right away is to get into the proper foundation garment.
Luckey’s has a number of them cut and seamed and fitted, even discreetly boned in certain instances—to give the trim, firm foundation that the mode requires.

3-: From Styles for the New Year, published in The News-Palladium (Benton Harbor, Michigan) of Wednesday 1^st January 1930:

Waistlines are definitely higher, and every woman who has one is emphasizing it. It is the youthful note in clothes. However, the woman who has the spare tire around her waistline is trying to disguise it by the bolero line, or a sophisticated cut which allows her a line at the hip as well as at the waistline.

4-: From Headlines, Waistlines Outlines And Skylines Keynotes of New Styles, published in the Daily Clarion-Ledger (Jackson, Mississippi) of Sunday 5^th January 1930:

Waist lines, if you please, are definitely higher, and every woman who has one is making good use of it. The puffy matron with a fondness for too much sweets and a spare tire around her midsection, is trying to disguise it by use of a sophisticated cut that allows her a line at the hips as well as the waist.

5-: From The Montgomery Advertiser (Montgomery, Alabama) of Sunday 13^th April 1930:

Spare Tire Around Mid Ribs Needs Quick Removal
By Antoinette Donnelly *

The season surely is a refined waistline one. If you have a little or a big spare tire hanging around your mid-ribs you might as well go into retreat until the dress designers think up another for us. Or else get busy on the midsection. It’s a terrible strain on the sensibilities of a lady to get the dress buckle locked only to find a “spare” above and below the belt.

* Antoinette Donnelly (1887-1964) was a U.S. newspaper advice columnist.

6-: From “Love’s Beauty Secrets”, by Laluna de Serrano, published in The Evening News (Harrisburg, Pennsylvania) of Friday 25^th April 1930:

Ladies, look to your waistlines! The new Paris fashions demand it. No longer can a straight line from shoulder to hip cover up that slight—or greater—roll around the middle. Waists are not to be pinched or waspish, but they are going to have a line or belt right around the middle of them, and, lo and behold, a bulge of “tummy” above or below, a “spare tire” around the sides looms out. So abdominal exercises to flatten the front, bending and twisting to smooth out the side rolls and perfect posture to remove the sway back, and you can step into the new models with confidence and pleasure.

 

IN BRITISH ENGLISH

 

1-: From the following advertisement, published in the Milngavie and Bearsden Herald (Milngavie, Dunbartonshire, Scotland) of Friday 13^th January 1933:

Have YOU a Spare Tyre Around the Waistline?

Incorrect Corset                                        Spencer Corset

The wrong corset will only emphasize the roll of flesh around the waistline. A Spencer, designed especially for you, will not only CONCEAL it, but will CORRECT it! Write for free study of your figure.

2-: From Corsets at their Best, by Madge Whiley, published in the Falkirk Herald (Falkirk, Stirlingshire, Scotland) of Wednesday 25^th January 1933:

It is a tremendous mistake to imagine that you are going to look as slim as a lamp-post by wearing a tight corset. Through this practice you may develop that ugly roll of fat above the top of the corset, or almost worse, what they call a “spare tyre” round the diaphragm. If you have a tendency to plumpness round the waistline, choose a corset which is long in the skirt, but short in front and well boned.

3-: From Women’s World, published in the Croydon Times (Croydon, London, England) of Saturday 19^th August 1933:

YOUR FIGURE
Choice of Well-fitting Clothes
CORRECT CORSETRY

Now that the lamp-post silhouette is a thing of the past and fashion again favours figures, it is important to take a critical look at what our mirrors show us. Do you see the gentle curves that modern frocks demand, or does your figure sag and bulge, and are there disconcerting “spare tyres” around the waist line?

4-: From Pointing the Way to Prettiness: Beauty’s Guide-Posts, published in the Morecambe Guardian and Heysham Observer (Morecambe, Lancashire, England) of Friday 10^th November 1933—here, spare tyre denotes a roll of fat around any part of the body:

The sleek slim mode of to-day and the sheath or tube frocks are merciless—unkindly revealing to fat rolls about the waist, “spare-tyres” round any part, or too generously proportioned hips.

5-: From Ladies’ Budget, by Jane Tudor, published in The Northern Herald (Bangor, County Down, Northern Ireland) of Saturday 25^th May 1935:

Don’t collapse in a heap, but sit well back in your chair. If you get into the habit of keeping your hips and back straight when standing or sitting, you will not develop that dreaded “spare tyre” round the waist.

6-: From London Lore: Fashion and Beauty Hints, by Jane Tudor, published in the Ballymena Observer and County Antrim Advertiser (Ballymena, County Antrim, Northern Ireland) of Friday 3^rd January 1936:

Here is a good way of keeping the waist supple, and removing any tendency to that dreaded “spare tyre” round one’s “middle.” Stand erect with hands on hips, slowly bend the body sideways to the left, slipping the hand down the side of the body while the right arm moves upwards. Raise body and bend to the other side, reversing the arm movement and reaching towards the right ankle. Continue with an easy swinging movement from side to side.

7-: From Beauty in a Hurry, by Eva Lorraine, published in the Falkirk Herald (Falkirk, Stirlingshire, Scotland) of Wednesday 8^th April 1936:

Do you pat? This is the modern way to beauty. Five minutes’ patting where it is needed will work wonders.
An adjustable patter into which are fitted club-shaped pieces of pliable rubber take astringent lotion, cleansing cream, or reducing ointment. Small patters serve adequately for patting away a double chin or working in the beneficial cleansing cream at night.
In the morning using the largest sized patter to massage away unwanted flesh on the hips, or the “spare tyre” around the waist. It reaches places which could not be reached by hand.

8-: From From the Top of a Bus, by ‘Josephine’, published in The Portadown News (Portadown, County Armagh, Northern Ireland) Saturday 8^th August 1936:

For those of us who are sensible enough to enjoy our food, here is good news! A system of muscle-control which leads eventually to figure-perfection is being introduced over here by Mrs. Inge Brandeis, a clever German woman who has made a special study of the subject.
[…]
Next week Mrs. Brandeis is to demonstrate her method to teachers at the New Education Fellowship conference at Cheltenham. The exercises, she tells me, are suitable for people of all ages who went [sic] to achieve muscle control and figure-perfection. She has had children of four as pupils and people of sixty and seventy. And—cheering news for those of us whose menfolk are developing “spare tyres” around the waistline—her method is equally successful for men.

9-: From Fashions Kind to the Tall Woman, by Jeanne de la Varre, published in the Western Mail and South Wales News (Cardiff, Glamorgan, Wales) of Wednesday 30^th September 1936:

Heaps of women are too thin above and too plump below: others have ugly bulges on the upper arms, and a “spare tyre” round the diaphragm.