Hello, Redfern, and welcome!
I think a background check is perfectly reasonable, and telling someone who has nothing to hide should not offend them. It is not "paranoid," it's SMART!!! Also, a strong man of integrity and good character would not be offended at your stating this upfront!
I no longer meet men on the internet sites, and have only done background check on one, several years ago. Background checks can reveal glaring discrepancies, but cannot reveal that someone is just a user or a loser in most cases. THAT is found out the hard way, and, unfortunately, I am speaking from experience.
I think your announcing the intention of a background check at the start is a good thing. You are "weeding out" the potential bad ones! You go, girl!!!
Seeker