Well, I'm almost ashamed to tell you that I tried this :), but it doesn't matter what character you use in the catenation, whether with join or interpolation into a string, it still causes the memory growth. I even tried calling a function to do the output, passing the values as a list and joining them inside the function, and still it occurs?

I do have a work around for you.

 print map{ $_, "\t" } $key1, $key2,
    $hash1{ $key1 }{ $key2 }, 
    $hash2{ $key1 }{ $key2 },
    $hash3{ $key1 }{ $key2 };
 print "\n";
[download]

Replace your print line with the above, and the memory growth will completely disappear. It isn't an exact replacement for the join, as you will get an extra tab at the end of the line. If that is a problem then you can go for manually interspersing the tabs:

 print $key1, "\t", $key2 "\t", 
    $hash1{ $key1 }{ $key2 }, "\t",
    $hash2{ $key1 }{ $key2 }, "\t",
    $hash3{ $key1 }{ $key2 }, "\n";
[download]

That both these avoid the memory growth indicates that the problem comes from building the single output string, which is something I guess, but this is bread and butter Perl code and it would surely have been noticed between 5.6.2 and now if it was that simple.

I have completely failed to reproduce the problem outside of two nested while loops accessing compound hashes using variables as keys. Every simplification I apply to reduce your code to a testcase and the problem disappears.

Anyway, I hope the above insights will allow you to get on with solving your problem; but do please raise a perlbug and let the guys that understand this stuff have a go at a proper solution/explanation.