Yes they could...Unless you think "too fat" is a protected class.Could a bakery refuse to make a cake for someone because they were "too fat"?
Sure, just say he was booked.Could a photographer refuse to photograph a wedding because the bride was "too ugly"?
Happens all the time...Ever been to a club with a doorman that picks who can go in?Could a hip coffee shop refuse to serve coffee to someone because they were "too old"?
Fact is that we discriminate all the time, in all walks of life...The good news is that creates more businesses to cater to those that are discriminated against...Now, do I think that all discrimination is good, or fair? No, of course not, and I think it rather stupid that anyone in business would turn down business. I mean after all the money is green. However, with that said we live in a free society, and I'd like to stay that way.
Matthew 10:34Think not that I am come to send peace on earth: I came not to send peace, but a sword.