A general strategy you can try here is "respond to amateurism with professionalism".  Even if it looks like he's being unreasonable (as it currently seems to you that he is), just suspend disbelief, and, in a completely non-confrontational manner, engage his questions as if they were serious.  "I always appreciate constructive criticism [true statement!  you don't have to say that his was constructive, let him think what he wants...maybe he actually did think it was].  I didn't quite understand what led you to wonder whether I did enough testing of X.  Did you see something in the results that made you suspect this specifically?  Just want to make sure I'm not missing anything.

Thanks for your input!"

Treat it exactly as if it were a sincere attempt to help, that you had a question about.  It's possible (though I'm thinking you think it unlikely) that he really is sincere and has something to offer you.  If so, wonderful!  You get useful feedback from someone smart!

If he doesn't actually have a real question, this technique may make that obvious in a relatively non-confrontational way.  Part of the value of it is that you are not simply being the victim of stalker-y behavior, but professionally and politely holding your ground.  It is to be hoped that this will lessen the feeling of exasperation that would otherwise normally accompany this kind of childish bullying, if that is indeed what it turns out to be.

There are very intelligent and successful people in academia who are nevertheless  woefully underdeveloped emotionally; one way this will be manifest is in the need to tear down other people who seem to be having success, or demonstrating skill, or garnering attention comparable to their own. This can catch one off guard when it's coming from a successful and respected person, because you would think that their success would be all they need to feel good about themselves.  That, alas, does not turn out to be true.  If it's a chronic emotional problem, you are unlikely to get him to change his behavior; hence the advice to concentrate specifically on blunting his ability to make his problem your problem.

If the cerebral approach doesn't work or becomes too time consuming, you can always set up a filter to send email from that address straight to trash....