Your situation sounds very confusing and doesn't really add up..
Your tenant has given you $11,500 already but hasn't signed anything?
How long ago did you agree to this?
Is the tenant a friend or relative of yours?
Does this tenant at least have a lease? Why would you arrange to use it on weekends, if you live in Florida? Please clarify if possible!
You definitely should consult with an attorney and also review any papers you may have signed, it is possible in some States that a verbal agreement with consideration may be binding, but I can not give any legal advice as I am not an attorney.. I could send you a list of lawyers here in Manhattan if you email me... Good Luck