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?