Often used as an imperative, the phrase to act, or to be, one’s age means to behave in a manner expected of, or appropriate to, a person of one’s age.

It also occurs in the humorous extension to act one’s age, and not one’s shoe size, and variants; the earliest occurrence that I have found is from Teen Message, published in the Philadelphia Daily News (Philadelphia, Pennsylvania) of Monday 24^th April 1967:

Tommy W.—Please grow up.—Susan.
[…]
A. E.—You belong to me.—B. E.
Wendy & Bobby—Happy Anniversary!—Lynne.
Joey D.—Act your age, and not your shoe size.—Carol.

This humorous extension also occurs in British English; the following is from Will our Joan act her age?, in the column Switched on, edited by Phil Penfold, entertainments editor, published in the Evening Chronicle (Newcastle upon Tyne, Northumberland) of Friday 8^th July 1988:

On Sunday, that aging television vamp Ms. Joan Collins¹ (in her mid-fifties if my calculations are correct) plays a young femme fatale singer-cum-Russian-spy in a mini-series called Monte Carlo.
I will ignore the unpleasant gag made by a colleague that at her age Ms. Collins ought to be playing the Count of Monte Cristo, but the expression “act your age instead of your shoe size” DID spring to mind.

¹ Joan Henrietta Collins (born 1933): English actress, author and columnist

The phrase to act one’s age, and not one’s shoe size has in turn been jocularly modified as to act one’s shoe size, and not one’s age, and variants; the earliest instance that I have found is from They have class in class, too, about Jackson High School’s basketball team, published in The Miami News (Miami, Florida) of Wednesday 26^th December 1973:

Bouton, the Jackson High assistant basketball coach, teaches an honors U.S. Government class every morning.
Three of the starters on Jackson’s undefeated (10-0) basketball team are enrolled in the class.
[…]
The government class is a spirited one. In between serious moments, Bouton keeps the class lively by wisecracking with the basketball-playing trio.
“I’ve practiced a routine so I can put them down,” says Bouton, laughing. “Usually, I’ll come over with a crack just to keep them in line. I’ll tell them that if they can’t act their age that they should at least try to act their shoe sizes.”

The following is from Lines on liberty, published in The Jackson Sun (Jackson, Tennessee) of Sunday 6^th July 1986:

Being an American on the Fourth of July is like being a child all over again. You get to do the crazy things you haven’t done in a long time. It’s like the old saying “act your age and not your shoe size.” Instead, you get to act your shoe size and not your age.
Clarice Sanders
Jackson

The jocular phrase to act one’s shoe size, and not one’s age also occurs in British English, as in this announcement published in The Stage (London) of Thursday 21^st November 1996:

CALLING TOY
BOYS & GIRLS
Can you act your shoe size and not your age?
Are you free from 25^th-29^th January ’97 for five
days work in central London?
Could you bring to life some of the most exciting
toy concepts in the business?
If the answer to these questions is ‘YES’ and you’re free
for an audition on 3^rd December, then please ring us
on 0181 296 9778 to find out more.

The noun shoe size is also used as a term of comparison in other humorous phrases; for example, the following is from High School Confidential, published in The Clarion-Ledger (Jackson, Mississippi) of Tuesday 26^th June 1979:

To Robbie M. of St. Andrews.: We’re watching out for you. From the two D’s.
To L. A.: Act your shoe size, not your head size. From you know who.
To Mike T. From David D.: I challenge you to a race around the block. If you don’t, I know you’re Chicken!!

On Thursday 13^th November 1986, The Stage (London) published this review of Soap, broadcast on Channel 4:

Soap, the wackiest show on American television, is back on screen after 20 months and the impenetrable saga involving the Tate and Campbell families goes on its nutty way.
For cult lovers, the show is a treasure but, for the uncommitted, don’t bother to try to sort out the characters or the story. This is the only show to have half the script made up of retelling what has gone before, and asking questions about what will happen next.
Jessica has fallen for El Puerco, a revolutionary, and they are adrift in the Caribbean until Billy, her son, in a wet suit (“a shining bald black man is your son?” asks El) saves them.
Gwen the hooker entertains a fast food faddist, Chester and Dutch buy a construction company with an IOU, and a carnival’s half-man, half-dog provides vital clues about Carol, who has eloped with a fire-eater.
Spike Milligan² would be proud of that lot, and even Monty Python³ makes better sense. If, to quote from Soap, you haven’t heard from your brain lately and have an IQ lower than your shoe size, then this is for you.

² Spike Milligan (Terence Alan Milligan – 1918-2002): Irish comedian and author who came to prominence in the cult radio programme The Goon Show (1951-59)
³ Monty Python: British comedy group who created the influential television series Monty Python’s Flying Circus (1969-74)