Ethically speaking, should private businesses be allowed to refuse service to
While I think you are right to observe that business owners are generally not allowed to discriminate against persons on the basis of their unchosen characteristics, it does not follow that they are allowed to discriminate on the basis of chosen characteristics. Religion, sexual orientation and political commitments are paradigm examples: they are chosen at least in their outward manifestations, but as a society we have decided not to rank people on the basis of such choices and to impose this non-discrimination upon businesses. This makes sense insofar as such choices are ones that the person is deeply identified with. They are part of a person's identity and, by refusing to serve a person on the basis of such a choice, or by requiring a person not to express such a choice as a condition of admittance, one is rejecting and disrespecting the whole person -- just as one is rejecting and disrespecting the whole person when one refuses to serve her on the basis of her gender or skin color.
The same does not typically hold when a business excludes those who wear no shoes, i.e. requires shoes as a condition of admittance. The choice to walk barefoot is a superficial choice, not part of a person's identity, and so the requirement to wear shoes is not demeaning or disrespectful (though it could be in special cases such as that of Mahatma Gandhi). Still, even with regard to such superficial choices, the business owner must still have a plausible reason for imposing the requirement. Business owners have a legitimate reason to preserve a certain ambiance in their establishment, and this may justify the exclusion of barefoot patrons and certainly the exclusion of those who spit on the floor. But this would not typically justify the exclusion of those who wear a belt or brown socks.
Obesity is an interesting case in that is has some features of unchosen characteristics: the obese person cannot suppress the outward manifestation of her obesity in the way people could remove any outward manifestations of their religion, sexual orientation or political commitments. Moreover, obesity is typically part of a person's identity, albeit sometimes an unwanted part; and so refusing admittance to a person on the basis of his obesity constitutes a rejection of, and disrespect for, the whole person.