I see two options here. #1 is potentially faster but might generate more communications. #2 is harder but will likely be more decisive.
Dear Annoying Contact
(or whatever his name is):
Thanks for your emails!
Things have really heated up here at My Awesome Company
(or whatever your company name is) and I just can't get away like I used to. I have to really save my socializing for rather specific occasions.
I truly appreciate your interest and wish you all the best.
(or whatever your standard closing salutation is),
(probably not your real name
It's nice. It's short. It closes off contact without smashing his ego and it also gives you an out in case he sees you at some event; that means it's a big deal event, so far as he is concerned. And being busy is maybe a little white lie sometimes, but it's also very true at other times, so you are covered there.
Or you could actually meet with him one time and let him down then. That's another option. Meet him, look at his resume while you're meeting him, give him a few pointers and then hand it back to him. Do not take it back with you; make certain he's got it back in his hands (a very heavy hint that you do not want it and you are closing off contact).
Plus by giving him some sort of pointer on his resume, you're actually giving him something valuable for the fifteen minutes or so you see him. And do make it no longer than fifteen minutes. You're busy, remember?
And in the meantime, a lot of us have been in his boat. I learned early to not push things more than twice (three times if it was someone I really figured could help me if they just gave me a chance), because you run the risk of annoying someone who you should be cultivating as an ally. Better for him to learn that but without you burning a bridge. Because he might have business for you (or know someone who does) in the future.