Good answer MedicineBow!
In fact, if I am on your property you can tell me to leave and don't even need a reason. If I don't leave I am trepassing. As someone has pointed out, in most places a merchant's establishment may come under some additional rules, some of which may include some type of "equal accomodation" statutes that may prevent the merchant from refusing service to someone. These, however are usually non-discrimination statutes. If TGIF's let's others wear OC guns but not you, you might have a case - depends on Virginia's laws. But if they prohibit everyone from carrying open in the restuarnt, that would come under the heading of "they would rather lose your business".
Did someone say that some states have laws that require merchants to serve gun toters?