I think you are confusing "Stand Your Ground" with "Castle Doctrine". My understanding of Florida's Stand Your Ground law is that one is not obligated to retreat from anyplace that one has a right to be, subject to exceptions if law-breaking is going on.
Stand Your Ground simply removes the obligation to retreat if a reasonable person would think it possible to do so safely. Stand Your Ground does not in any other way change the circumstances in which self-defense is justified, including self-defense with a deadly weapon.
The Sheriff has the cart before the horse. If he wanted to say something meaningful, then he should have stated that self-defense with a deadly weapon was not justified. In such a case, Stand Your Ground is irrelevant.
As for whether the "No Weapons" sign changes anything, that depends very much on the state's weapons and trespassing laws. In Texas, for example, if you wish to exclude people carrying concealed weapons, you are obligated to post signs at all entrances and there are specific wording and formatting requirements. Otherwise, the sign has no effect.
Furthermore, there are additional laws which permit the carrying of weapons by ex-cops which may or may not have permitted the shooter to have his weapon in the theater. Other than the shooting, did the shooter break any laws that would have excluded him from Stand Your Ground protection?
If the theatre manager found out that he had a weapon on him in violation of theatre policy and told him to leave the theatre, did he have the right to stand his ground and refuse to move and pull out his weapon and shoot the manager forcing him to retreat to the door out??
A theatre is not your home or your car or even a public sidewalk that you might have a right to.
Your right to your seat in a theatre can be revoked by management at any time especially if you breach their No Weapons Allowed policy.
You need to rethink your argument.