Much cleaner! Putting the increment back in and not skipping a line at the end yields a "more intresting"* result (63 chars):

perl -ln0e's/\s+/ /g;print$"x(40-($c=2+length$&)/2),$&while/.{0$c,}? |
+.+/g' a.txt w.txt
                                      a 
                                    a a a 
                                  a a a a a 
                                a a a a a a a 
                              a a a a a a a a a 
                             a a a a a a a a a a 
                          The same principle applies 
                    to any text file, basically splitting 
                      words only on spaces or new lines 


perl -ln0e's/\s+/ /g;print$"x(40-($c=2+length$&)/2),$&while/.{0$c,}? |
+.+/g' w.txt a.txt
                                     The 
                                same principle 
                             applies to any text 
                          file, basically splitting 
                      words only on spaces or new lines 
                    a a a a a a a a a a a a a a a a a a a 
                       a a a a a a a a a a a a a a a a
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(I know, I know. I'm the only one who could possibly still be interested at this point.)

* update "more interesting" meaning more <|triangular|>  (than the original challenge).

And, moving even deeper into 'useless use of code in void context':

print($"x(40-($c=2+length$&)/2),$&),$c*=($c<80)while...
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will make triangles of files of any length (a step towards automated obfusification?).

p