I'm not sure if it is relevant--you may be aware already--but I added a couple of printfs to your code:

SV * _copy( SV * arg_obj, SV * second, SV * third ) {
     Number * num_obj;
     SV * obj_ref, * obj;
     printf( "_copy:%p %p %p\n", arg_obj, second, third  );
...

SV * _set_from_existing( SV * arg_obj ) {
     Number * num_obj;
     SV * obj_ref, * obj;
     printf( "_set::%p\n", arg_obj );

...
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And it appears that the overloading is not causing your _copy() function to be called:

Finished Build Compile Stage

_set::0185E260
555
113
Destroying ...... destroyed
Destroying ...... destroyed
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Which (as best I can tell) explains the output completely:

$$num1 = Grief::new( 113 );
$num2 = $num1; # Assign using _copy( )
$num3 = _set_from_existing( $num1 ); # Assign using _set_from_existing
+( )
_set_val( $num1, 555 );
print _get_val( $num2 ),"\n", _get_val( $num3 ), "\n";
__END__
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$num2, in the absence of the overloading is simply an alias to $num1, whereas $num3 is explicitely as new object with the same value. When you set $num1 to 555, you are also setting $num2, as they are both references to the same object.

All of which is probably not news to you. The only real question as far as I can see is if overload can't or won't allow you to overload assignment, why doesn't use overload '=' => \&_copy; throw an error?

And it appears that the overloading is not causing your _copy() function to be called

Damn!! ... that's the oversight I was ... ummmm ... overlooking. I should've thought to stick a printf() in there as a check. Thanks for picking that up.

Another approach is to simply comment out the 'use overload ...' code - which has no effect on the output of the script at all. Oh, well .... live and learn ....

why doesn't use overload '=' => \&_copy; throw an error?

Good question. Thanks BrowserUK.

Cheers,
Rob
Update: I think, at last, I start to see the light. The overloading of the assignment operator takes its effect only when the value of either $num1 or $num2 is subsequently altered using an overloaded operator. Consider the following:

use warnings;
use Devel::Peek;

package Grief;
use overload
    '++'   => \&_inc,
    '='    => \&_copy,
;


use Inline C => Config =>
    BUILD_NOISY => 1;

use Inline C => <<'EOC';

typedef struct {
    long num;
} Number;

SV * new(SV * x) {
     Number * num_obj;
     SV * obj_ref, * obj;

     New(1, num_obj, 1, Number);
     if(num_obj == NULL)
      croak("Failed to allocate memory in new() function");
     obj_ref = newSViv(0);
     obj = newSVrv(obj_ref, "Grief");
     num_obj->num = SvUV(x);

     sv_setiv(obj, (IV)num_obj);
     SvREADONLY_on(obj);
     return obj_ref;
}

SV * _get_val(SV * obj) {
     return newSVuv(((Number*)SvIV(SvRV(obj)))->num);
}

void _inc(SV * obj, SV * second, SV * third) {
     (((Number*)SvIV(SvRV(obj)))->num)++;
}

SV * _copy(SV * arg_obj, SV * second, SV * third) {
     Number * num_obj;
     SV * obj_ref, * obj;
     printf( "_copy:%p %p %p\n", arg_obj, second, third  );
     New(1, num_obj, 1, Number);
     if(num_obj == NULL)
      croak("Failed to allocate memory in _copy() function");
     obj_ref = newSViv(0);
     obj = newSVrv(obj_ref, "Grief");
     num_obj->num = ((Number*)SvIV(SvRV(arg_obj)))->num;

     sv_setiv(obj, (IV)num_obj);
     SvREADONLY_on(obj);
     return obj_ref;
}

void DESTROY(SV * obj) {
    printf("Destroying ...");
    Number * number = (Number*)SvIV(SvRV(obj));
    Safefree(number);
    printf("... destroyed\n");
}


EOC

$num1 = Grief::new(113);
$num2 = $num1;
$num3 = _copy($num1, '', '');

#Run any one of the following 4 lines
$num1++; # _copy() gets called, 3 objects DESTROYed
#$num2++; # _copy() gets called, 3 objects DESTROYed
#_inc($num1, '', ''); # no _copy(), 2 objects DESTROYed
#_inc($num2, '', ''); # no _copy(), 2 objects DESTROYed

print _get_val($num2)," | ", _get_val($num3), "\n";
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