it will become a self-fulfilling prophecy if you snoop on him and keep that up because he'll feel that you think he's cheating and figure that he may as well since you think of him that way.
the only solution that lasts, as in sort out the problem, the reason instead of just the symptoms, is to let go of wanting to change him and to let go of the wants for approval, control, security etc that are making you snoop around.
it's about you, not him.
check out the sedona method stuff -found that really helpful in releasing wants.
Sedona Method (official site) The Secret self-help program; self-improvement technique
i also run a website on personal development, you might find this article on focus helpful and could just "zoom out" next time an urge to snoop comes up
How to Focus: Get Things Done and Be Free
also check out the work of eckhart tolle, specifically "the power of now".
hope that helps
alex