I don't see much of an issue. A "fat" wallet doesn't necessarily indicate that there is anything of value in it. It might be filled with coupons, supermarket loyalty cards and $1 bills. People carrying large amounts of cash are more likely to have it in a purse or handbag.

If you are worried, just put your wallet in your carry-on before you get to the security checkpoint. You could make it a habit of doing so as soon as you exit your car or pay for the shuttle/taxi.