How safe is my patio and how much weight could it support?
This really needs to be looked at by a structural engineer, or similar qualified person, to give you a load bearing range.  To calculate the load one would need to factor in the size of the wood, the type of the wood, condition of the wood (rot, ...) the overall weight of the structure, and how it is secured to the structure.  I can speak from experience that balconies do collapse from overloading and poor maintenance.  Where I live they had one collapse about 10 years ago and many got hurt.  The codes had to be updated and new rules were made for enforcing them.