Hi,
I am not insecure as well, but I would NEVER let my boyfriend look at it! (and no he is not secretly doing it behind my back =P )
I would feel totally uncomfortable.. and if it makes YOU feel uncomfortable then he should respect that and not look and read those articles.
I feel like guys should feel that their girlfriends/wives are the most beautiful women, inside and out and SHOULD not be looking at those magazines if they are in a committed relationship!!
You should tell him that if it makes you feel unhappy and maybe more insecure, then why is he doing it. If he knows you are already insecure, he is making it worse. Sorry, but I think what he is doing is wrong.
Good luck to you~!