I am not experienced enough to know most of the inner details, but it's fair to say that perl does a lot of work internally when the items are first accessed. If you change to Devel::Peek, you can see how the structure changes after access:

use strict;
use warnings;
use Devel::Peek qw(Dump);

my $s = 'AAAAAAAAAAAAAAA';

my %hash = map {$s++ => 1} 1 .. 2;

print "before:\n";
Dump \%hash;


open my $fh, '>', 'j1.txt' or die $!;

for my $key (keys %hash) {
    print $fh "$key $hash{$key}\n";
}

print "after:\n";

Dump \%hash;

[download]

Output:

before:
SV = IV(0x1e5cca8) at 0x1e5ccb8
  REFCNT = 1
  FLAGS = (TEMP,ROK)
  RV = 0x1e88420
  SV = PVHV(0x1e63ef0) at 0x1e88420
    REFCNT = 2
    FLAGS = (PADMY,SHAREKEYS)
    ARRAY = 0x1ed7880  (0:6, 1:2)
    hash quality = 125.0%
    KEYS = 2
    FILL = 2
    MAX = 7
    Elt "AAAAAAAAAAAAAAA" HASH = 0xa39c9065
    SV = IV(0x1e7a9a8) at 0x1e7a9b8
      REFCNT = 1
      FLAGS = (IOK,pIOK)
      IV = 1
    Elt "AAAAAAAAAAAAAAB" HASH = 0x7747aa6e
    SV = IV(0x1e7a990) at 0x1e7a9a0
      REFCNT = 1
      FLAGS = (IOK,pIOK)
      IV = 1

after:
SV = IV(0x1e883e0) at 0x1e883f0
  REFCNT = 1
  FLAGS = (TEMP,ROK)
  RV = 0x1e88420
  SV = PVHV(0x1e63ef0) at 0x1e88420
    REFCNT = 2
    FLAGS = (PADMY,OOK,SHAREKEYS)
    ARRAY = 0x1e75110  (0:6, 1:2)
    hash quality = 125.0%
    KEYS = 2
    FILL = 2
    MAX = 7
    RITER = -1
    EITER = 0x0
    RAND = 0x69863a90
    Elt "AAAAAAAAAAAAAAA" HASH = 0xa39c9065
    SV = PVIV(0x1e7f860) at 0x1e7a9b8
      REFCNT = 1
      FLAGS = (IOK,POK,pIOK,pPOK)
      IV = 1
      PV = 0x1ed7810 "1"\0
      CUR = 1
      LEN = 16
    Elt "AAAAAAAAAAAAAAB" HASH = 0x7747aa6e
    SV = PVIV(0x1e7f878) at 0x1e7a9a0
      REFCNT = 1
      FLAGS = (IOK,POK,pIOK,pPOK)
      IV = 1
      PV = 0x1e98b90 "1"\0
      CUR = 1
      LEN = 16

[download]

Here's a brief on memory usage.

In reply to Re: Devel::Size reports different size after hash access by stevieb
in thread Devel::Size reports different size after hash access by Cristoforo

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